**Research interests: Associative
rings; Automata and formal languages; Combinatorics on words;
Computational complexity; Group representations; Non-associative rings;
Semigroups; Universal algebra**

**Citation indices: RISC
(Russian Index of Scientific Citation), **Google
citation, MathSciNet,
**Scopus**,
**Web of Science**

13. Synchronization of finite automata, Uspekhi Matematicheskikh Nauk (2022), no.5(467), 53-130 [Russian; English translation Russian Mathematical Surveys (2022) 77, no. 5, 819-891].

12. (with J. Kari) Černý's conjecture and the road colouring problem, Chapter 15 in J.-É. Pin (ed.), Handbook of Automata Theory, Vol. I. European Mathematical Society, Zürich, 2021, 525-565.

11. (with L.N. Shevrin and B.M. Vernikov) Lattices of semigroup varieties, Izv. VUZ. Matematika (2009) no.3, 3-36 [Russian; English translation: Russian Mathematics (Iz. VUZ) (2009) 53, no.3, 1-28].

10. Synchronizing automata and the Černý conjecture, in C. Martín-Vide, F. Otto, H. Fernau (eds.), Language and Automata Theory and Applications. LATA 2008 [Lect. Notes Comp. Sci., 5196], Springer-Verlag, Berlin-Heidelberg-N.Y., 2008, 11-27

9. Synchronizing automata and the Černý conjecture, in Pre-proc. 2nd Int. Conf. on Language and Automata Theory and Applications, Research Group on Mathematical Linguistics, Report 36/08, Universitat Rovira i Virgili, Tarragona, 2008, 23-42.

8. Lev Naumovich Shevrin: fifty years in the service of mathematics, Semigroup Forum, 2008, 76, no.2, 185-191.

7. (with D. S. Ananichev, I. V. Petrov) Collapsing words: a progress report, Int. J. Foundations Comp. Sci. (2006) 17, no.3, 507-518.

6. (with D. S. Ananichev, I. V. Petrov) Collapsing words: a progress report, in C. de Felice, A. Restivo (eds.), Developments in Language Theory, Proc. 9th Int. Conf. DLT 2005 [Lect. Notes Comp. Sci. 3572], Springer-Verlag, Berlin-Heidelberg-N.Y., 2005, 11-21.

5. Gyorgy Pollák's work on the theory of semigroup varieties: Its significance and its influence so far, Acta Sci. Math. Szeged (2002) 68, no.3-4, 875-894.

4. Some open problems concerning relatively free and free profinite semigroups, Semigroup Forum (2002) 64, no.2, 224-235.

3. The finite basis problem for finite semigroups, Math. Japonica (2001), 53, no.1, 171-199. (

The link refers to a version of the survey that is occasionally updated. The latest update: July 2014, 3.3 Mb)2. The finite basis problem for finite semigroups: a survey, in P. Smith, E. Giraldes, P. Martins (eds.), Semigroups, World Scientific, Singapore, 2000, 244-279.

1. (with L. N. Shevrin) Identities of semigroups, Izv. VUZ. Matematika (1985) no.11, 3-47 [Russian; English translation Soviet Math Izv. VUZ (1985) 29, no.11, 1-64].

*2024-2020 (170-150) * *2019-2015 (149-134) 2014-2010 (133-120) 2009-2005 (119-94)*

*2004-2000 (93-66) * *1999-1994 (65-46) 1993-1984 (45-18) 1983-1977 (17-1)*

170. (with D. F. Casas Torres) Don's conjecture for binary completely reachable automata: an approach and its limitations (accepted); see preprint

169. (with S. V. Gusev and O. B. Sapir) Strongly nonfinitely based monoids (submitted); see preprint

168. (with I. Dolinka and S. V. Gusev) Semiring and involution identities of powers of inverse semigroups, Comm. Algebra (2024), 52, no. 5, 1922-1929.

167. Synchronization of primitive automata, RAIRO Theor. Informatics and Applications (2024), 58, Article no. 3.

166. (with N. V. Kitov) Identities in twisted Brauer monoids, in A. A. Ambily, V. B. Kiran Kumar (eds.), Semigroups, Algebras and Operator Theory [Springer Proc. Math. Statistics, 436], Springer Singapore, 2024, 79-103

165. (with S. V. Gusev) Semiring and involution identities of power groups, J. Australian Math. Soc. (2023), 115, no.3, 354-374.

164. (with E. A. Bondar and D. F. Casas Torres) Completely reachable automata: an interplay between automata, graphs, and trees, Int. J. Foundations Comp. Sci. (2023), 34, no.6, 655-690.

163. (with O. B. Sapir) Catalan monoids inherently nonfinitely based relative to finite R-trivial semigroups, J. Algebra (2023), 633, 138-171.

162. (with S. V. Gusev) Semiring identities of finite inverse semigroups, Semigroup Forum (2023), 106, no.2, 403-420.

161. Remark on the identities of the grammic monoid with three generators, Semigroup Forum (2023), 106, no.1, 332-337.

160. (with P. A. Azeef Muhammed and K. Auinger) Cross-connection structure of locally inverse semigroups, Int. J. Algebra and Computation (2023), 33, no. 1, 123-159.

159. (with D. F. Casas Torres) Binary completely reachable automata, in A. Castaneda, F. Rodriguez-Henriquez (eds.), LATIN 2022: Theoretical Informatics [Lect. Notes Comp. Sci. 13568], Springer, Cham, 2022, 345-358

158. Synchronization of finite automata, Uspekhi Matematicheskikh Nauk (2022), no.5(467), 53-130 [Russian; English translation Russian Mathematical Surveys (2022) 77, no. 5, 819-891].

157. Identities of the stylic monoid, Semigroup Forum (2022), 105, no. 1, 345-349.

156. (with Hanan Shabana) Optimal synchronization of partial deterministic finite automata, Acta Informatica (2022), 59, no. 4, 479-504.

155. (with P. A. Azeef Muhammed) A tale of two categories: Inductive groupoids and cross-connections, J. Pure Appl. Algebra (2022), 226, no.7, Article no. 106940.

154. (with J. Kari) Černý's conjecture and the road colouring problem, Chapter 15 in J.-É. Pin (ed.), Handbook of Automata Theory, Vol. I. European Mathematical Society, Zürich, 2021, 525-565., 525-565.

153. Semiring identities of the Brandt monoid, Algebra Universalis (2021), 82, no. 3, Article no. 42.

152. (with Azza M. Gaysin) Block-groups and Hall relations, in A.R.Rajan, M.V. Volkov, P. G. Romeo (eds.), Semigroups, Categories, and Partial Algebras [Springer Proc. Math. Statistics, 345], Springer Singapore, 2021, 25-32

151. (with N. V. Kitov) Identities of the Kauffman monoid K_4 and of the Jones monoid J_4, in A. Blass, P. Cégielski, N. Dershowitz, M. Droste, B. Finkbeiner (eds.), Fields of Logic and Computation III, Essays Dedicated to Yuri Gurevich on the Occasion of His 80th Birthday [Lect. Notes Comp. Sci., 12180], Springer, Cham, 2020, 156-178.

150. (with Yuzhu Chen, Xun Hu, N. V. Kitov, and Yanfeng Luo) Identities of the Kauffman monoid K_3, Comm. Algebra (2020) 48, no.5, 1956-1968.

149. Identities in Brandt semigroups, revisited, Ural Math. J. (2019) 5, no.2, 80-93.

148. Slowly synchronizing automata with idempotent letters of low rank, J. Automata, Languages and Combinatorics (2019) 24, no. 2-4, 375-386.

147. (with Hanan Shabana) Using Sat solvers for synchronization issues in partial deterministic automata, in I. Bykadorov, V. A. Strsuevich, T. Tchemisova (eds.), Mathematical Optimization Theory and Operations Research. 18th Int. Conf. MOTOR 2019, Revised Selected Papers [Comm. Comp. Information Sci. 1090], Springer, Cham, 2019, 103-118.

146. (with H. Fernau, V. Gusev, S. Hoffmann, M. Holzer, and Petra Wolf) Computational complexity of synchronization under regular constraints, in P. Rossmanith, P. Heggernes, J.-P. Katoen (eds.), Mathematical Foundations of Computer Science. MFCS 2019 [Leibniz Int. Proc. Informatics 138], Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, 2019, 63:1-63:14

145. The identities of the free product of a pair of two-element monoids, Algebra Universalis (2019) 80, no.1, 14:1-14:6.

144. (with F. Gonze, V. Gusev, B. Gerencser, and R. M. Jungers) On the interplay between Černý and Babai's conjectures, Int. J. Foundations Comp. Sci. (2019) 30, no.1, 93-114.

143. (with P. A. Azeef Muhammed) Inductive groupoids and cross-connections of regular semigroups, Acta Math. Hungarica (2019) 157, no.1, 80-120.

142. (with E. A. Bondar) A characterization of completely reachable automata, in M. Hoshi, S. Seki (eds.), Developments in Language Theory. DLT 2018 [Lect. Notes Comp. Sci. 11088], Springer, Cham , 2018, 145-155.

141. (with Hanan Shabana) Using Sat solvers for synchronization issues in non-deterministic automata, Siberian Electronic Math. Reports (2018) 15, 1426-1442.

140. (with P. V. Silva and F. Soares) Local finiteness for Green's relations in semigroup varieties, Comm. Algebra (2018) 46, no.11, 4625-4653.

139. (with F. Gonze, V. Gusev, B. Gerencser, and R. M. Jungers) On the interplay between Babai and Černý's conjectures, in E. Charlier et al. (eds.), Developments in Language Theory. DLT 2017 [Lect. Notes Comp. Sci. 10396], Springer, Berlin-Heidelberg-N.Y., 2017, 185-197.

138. (with L.M.Shneerson) The identities of the free product of two trivial semigroups, Semigroup Forum (2017) 95, no.1, 245-250.

137. (with E.A.Bondar) Completely reachable automata, in C. Campeanu, F. Manea, J. Shallit (eds.), Descriptional Complexity of Formal Systems. DCFS 2016 [Lect. Notes Comp. Sci. 9777], Springer, Berlin-Heidelberg-N.Y., 2016, 1-17 (see also expanded version).

136. (with D. N. Ashikmin and Wen Ting Zhang) The finite basis problem for Kiselman monoids, Demonstratio Mathematica (2015) 48, no.4, 475-492.

135. A nonfinitely based semigroup of triangular matrices, in J. Meakin, A.R.Rajan, P. G. Romeo (eds.), Semigroups, Algebra and Operator Theory [Springer Proc. Math. & Statistics. 142], Springer India, New Delhi-Heidelberg-N.Y.-Dordrecht-London, 2015, 27-38.

134. (with K. Auinger, Yuzhu Chen, Xun Hu, and Yanfeng Luo) The finite basis problem for Kauffman monoids, Algebra Universalis (2015) 74, no.3-4, 333-350.

133. (with K. Auinger, I. Dolinka, and T. V. Pervukhina) Unary enhancements of inherently nonfinitely based semigroups, Semigroup Forum (2014) 89, no.1, 41-51.

132. (with F. M. Fominykh and P. V. Martyugin) P(l)aying for synchronization, Int. J. Foundations Comp. Sci. (2013) 24, no.6, 765-780.

131. (with D. S. Ananichev and V. V. Gusev) Primitive digraphs with large exponents and slowly synchronizing automata, Zapiski Nauchnyh Seminarov POMI [Combinatorics and Graph Theory. IV] (2012) 402, 9-39 [Russian, English translation J. Math. Sci. (2013) 192, no.3, 263-278].

130. (with K. Auinger and I. Dolinka) Equational theories of semigroups with involution, J. Algebra (2012) 369, 203-225.

129. (with F. M. Fominykh) P(l)aying for synchronization, in N. Moreira, R. Reis (eds.), Implementation and Application of Automata. Proc. 17th Int. Conf. CIAA 2012 [Lect. Notes Comp. Sci. 7381], Springer, Berlin-Heidelberg-N.Y., 2012, 159-170.

128. (with K. Auinger and I. Dolinka) Matrix identities involving multiplication and transposition, J. Europ. Math. Soc. (2012) 14, no. 3, 937-969.

127. (with E. W. H. Lee) Limit varieties generated by completely 0-simple semigroups, Int. J. Algebra and Computation (2011) 21, no.1-2, 257-294.

126. (with S. V. Goldberg and S. I. Kublanovsky) A minimal non finitely based semigroup whose variety is polynomially recognizable, Fundamentalnaya i prikladnaya matematika (2010) 16, no. 3, 105-122 [Russian, English translation J. Math. Sci. (2011) 177, no.6, 847-859].

125. (with J. Almeida, S. W. Margolis, and B. Steinberg) Characterization of group radicals with an application to Mal'cev products, Illinois J. Math. (2010) 54, no.1, 199-221.

124. (with D. S. Ananichev and V. V. Gusev) Slowly synchronizing automata and digraphs, in A. Kučera, P. Hlinéný (eds.), Mathematical Foundations of Computer Science [Lect. Notes Comp. Sci., 6281], Springerg, Berlin-Heidelberg-N.Y., 2010, 55-65.

123. (with M. Jackson) The algebra of adjacency patterns: Rees matrix semigroups with reversion, in A. Blass, N. Dershowitz, W. Reisig (eds.), Fields of Logic and Computation, Essays Dedicated to Yuri Gurevich on the Occasion of His 70th Birthday [Lect. Notes Comp. Sci., 6300], Springer, Berlin-Heidelberg-N.Y. 2010, 414-443.

122. (with V. H. Fernandes) On divisors of semigroups of order-preserving mappings of a finite chain, Semigroup Forum (2010) 81, no.3, 551-554.

121. A reduction theorem for associative ring varieties whose subvariety lattice is distributive, Discussiones Mathematicae, General Algebra and Applications (2010) 30, no.1, 119-132.

120. (with D. Easdown and M. V. Sapir) Periodic elements of the free idempotent generated semigroup on a biordered set, Int. J. Algebra and Computation (2010) 20, no.2, 189-194.

119. Synchronizing automata preserving a chain of partial orders, Theor. Comput. Sci. (2009) 410, no.37, 3513-3519.

118. (with I. A. Mikhailova) Patterns avoidance by palindromes, Theor. Comput. Sci. (2009) 410, no.30-32, 2992-2998.

117. (with M. Jackson) Undecidable problems for completely 0-simple semigroups, J. Pure Appl. Algebra (2009) 213, no.10, 1961-1978.

116. (with J. Almeida, S. W. Margolis, and B. Steinberg) Representation theory of finite semigroups, semigroup radicals and formal language theory, Trans. Amer. Math. Soc. (2009) 361, no.3, 1429-1461.

115. (with M. Jackson) Relatively inherently nonfinitely q-based semigroups, Trans. Amer. Math. Soc. (2009) 361, no.4, 2181-2206.

114. (with L.N. Shevrin and B.M. Vernikov) Lattices of semigroup varieties, Izv. VUZ. Matematika (2009) no.3, 3-36 [Russian; English translation Russian Mathematics (Iz. VUZ) (2009) 53, no.3, 1-28].

113. Synchronizing automata and the Černý conjecture, in C. Martín-Vide, F. Otto, H. Fernau (eds.), Language and Automata Theory and Applications. LATA 2008 [Lect. Notes Comp. Sci., 5196], Springer, Berlin-Heidelberg-N.Y., 2008, 11-27.

112. (with J. Almeida and S.V. Goldberg) Complexity of the identity checking problem in finite semigroups, Zapiski Nauchnyh Seminarov POMI [Studies in Constructive Mathematics and Mathematical Logic. XI] (2008) 358, 5-22[Russian; English translation: J. Math. Sci. (2009) 158, no.5, 605-614].

111. Synchronizing automata and the Černý conjecture, in Pre-proc. 2nd Int. Conf. on Language and Automata Theory and Applications, Research Group on Mathematical Linguistics, Report 36/08, Universitat Rovira i Virgili, Tarragona, 2008, 23-42.

110. (with D. S. Ananichev and Yu. I. Zaks) Synchronizing automata with a letter of deficiency 2, Theor. Comp. Sci. (2007) 376, no.1-2, 30-41.

109. (with E. W. H. Lee) On the structure of the lattice of combinatorial Rees-Sushkevich varieties, in J.M.Andre e.a. (eds.), Proc. Int. Conf. "Semigroups and Formal Languages'' in honour of the 65th birthday of Donald B. McAlister, World Scientific, Singapore, 2007, 164-187.

108. Synchronizing automata preserving a chain of partial orders, in J. Holub, J.Zdarek (eds.), Implementation and Application of Automata. Proc. 12th Int. Conf. CIAA 2007 [Lect. Notes Comp. Sci. 4783], Springer, Berlin-Heidelberg-N.Y., 2007, 27-37.

107. (with I. A. Mikhailova) Patterns avoidance by palindromes, in P. Arnoux, N.Bedaride, J. Cassaigne (eds.), WORDS 2007. Proc. 6th Int. Conf. on Words, Institute de Mathematiques de Luminy, Marseille, 2007, 212-221.

106. (with D. S. Ananichev and I. V. Petrov) Collapsing words: a progress report, Int. J. Foundations Comp. Sci. (2006) 17, no.3, 507-518.

105. (with D. S. Ananichev and Yu. I. Zaks) Synchronizing automata with a letter of deficiency 2, in O. H. Ibarra, Zhe Dang (eds.), Developments in Language Theory, Proc. 10th Int. Conf. DLT 2006 [Lect. Notes Comp. Sci. 4036], Springer, Berlin-Heidelberg-N.Y., 2006, 433-442.

104. (with F. Pastijn) D-compatible varieties of semigroups, J. Algebra (2006) 299, no.1, 62-93.

103. (with F. Pastijn) Cryptic varieties of semigroups, Semigroup Forum (2006) 72, no.2, 159-189.

102. (with B. M.Vernikov) Modular elements of the lattice of semigroup varieties, II, Contrib. Gen. Algebra (2006) 17, 171-188.

101. (with J. Almeida) Subword complexity of profinite words and subgroups of free profinite semigroups, Int. J. Algebra and Computation (2006) 16, no.2, 221-258.

100. (with J. Almeida and S. W. Margolis) The pseudovariety of semigroups of triangular matrices over a finite field, RAIRO Theor. Informatics and Applications (2005) 39, no.1, 31-48.

99. Modular elements of the lattice of semigroup varieties, Contrib. Gen. Algebra (2005) 16, 275-288.

98. (with D. S. Ananichev and I. V. Petrov) Collapsing words: a progress report, in C. de Felice, A. Restivo (eds.), Developments in Language Theory, Proc. 9th Int. Conf. DLT 2005 [Lect. Notes Comp. Sci. 3572], Springer, Berlin-Heidelberg-N.Y., 2005, 11-21.

97. On a question by Edmond W. H. Lee, Izvestija Ural'skogo Universiteta. Matematika i Mekhanika (2005) no.36, 167-178.

96. (with J. Almeida, S. W. Margolis, and B. Steinberg) Modular and threshold subword counting and matrix representations of finite monoids, in S. Brlek, C. Reutenauer (eds.), Words 2005, 5th Int. Conf. on Words, 13-17 September 2005, Acts, Publications du Laboratoire de Combinatoire et d'Informatique Mathematique, UQAM 36 (2005) 65-78.

95. (with F. Pastijn) R-compatible varieties of semigroups, Acta Sci. Math. (Szeged) (2005) 71, no.3-4, 521-554.

94. (with D. S. Ananichev) Synchronizing generalized monotonic automata, Theor. Comp. Sci. (2005) 330, no.1, 3-13.

93. (with D. S. Ananichev) Synchronizing monotonic automata, Theor. Comp. Sci. (2004) 327, no.3, 225-239.

92. Reflexive relations, extensive transformations and piecewise testable languages of a given height, Int. J. Algebra and Computation (2004) 14, no.5-6, 817-827.

91. (with D. S. Ananichev) Some results on Černý type problems for transformation semigroups, in I. Araýjo e.a. (eds.), Semigroups and Languages, World Scientific, Singapore, 2004, 23-42.

90. (with I. A. Goldberg) The finite basis problem for monoids of triangular boolean matrices, in Algebraic Systems, Formal Languages, and Conventional and Unconventional Computation Theory [Surikaisekikenkyusho Kokyuroku 1366], Research Institute for Mathematical Sciences, Kyoto University, 2004, 205-214. (

One of the claims in the paper is wrong. Namely, Theorem 2.1 claims that the monoid $TB_n$ of all triangular Boolean matrices is inherently nonfinitely based if and only if $n>3$. In fact, the monoid $TB_3$ is inherently nonfinitely based as well; this has been shown by Li and Luo (cf. Li, J.R., Luo, Y.F.: On the finite basis problem for the monoids of triangular boolean matrices. Algebra Universalis (2011) 65, 353-362). Li and Luo have also checked that the monoid $TB_2$ is finitely based.)89. (with S. Margolis and J.-É. Pin) Words guaranteeing minimum image, Int. J. Foundations Comp. Sci. (2004) 15, no.2, 259-276.

88. (with B. M. Vernikov) Semimodular and arguesian semigroup varieties: a complete description, Izvestija Ural'skogo Universiteta. Matematika i Mekhanika (2004) no.30, 5-36 [Russian].

87. Checking quasi-identities in a finite semigroup may be computationally hard, Studia Logica (2004) 78, no.1-2, 349-356.

86. (with G. V. Tanana) On sums of radical and regular rings, Fundamentalnaya i prikladnaya matematika (2003) 9, no.1, 71-75 [Russian; English translation J. Math. Sciences (2005) 128, no.6, 3378-3380].

85. (with D. S. Ananichev and A. Cherubini) Image reducing words and subgroups of free groups, Theor. Comp. Sci. (2003) 307, no.1, 77-92.

84. (with D. F. Cowan, N. R. Reilly, and P. G. Trotter) The finite basis problem for quasivarieties and pseudovarieties generated by regular semigroups. I. Quasivarieties generated by regular semigroups, J. Algebra (2003) 267, no.2, 635-653.

83. (with S. Margolis and J.-É. Pin) Words guaranteeing minimal image, in M. Ito, T. Imaoka (eds.), Words, Languages and Combinatorics. III, World Scientific, Singapore, 2003, 297-310.

82. (with D. S. Ananichev) Synchronizing monotonic automata, in Z. Ésik, Z. Fülöp (eds.), Developments in Language Theory, Proc. 7th Internat. Conf. DLT 2003 [Lect. Notes Comp. Sci. 2710], Springer, Berlin-Heidelberg-N.Y., 2003, 111-121.

81. (with J. Almeida) Profinite identities for finite semigroups whose subgroups belong to a given pseudovariety, J. Algebra and its Applications (2003) 2, no.2, 137-163

80. (with I. A. Goldberg) Identities of semigroups of triangular matrices over finite fields, Mat. Zametki (2003) 73, no.4, 502-510 [Russian; English translation Math. Notes (2003) 73, no.4, 474-481].

79. (with D. S. Ananichev and A. Cherubini) An inverse automata algorithm for recognizing 2-collapsing words, in M. Ito, M. Toyama (eds.), Developments in Language Theory, 6th Internat. Conf. DLT 2002 [Lect. Notes Comp. Sci. 2450], Springer, Berlin-Heidelberg-N.Y., 2003, 270-282.

78. (with J. Almeida) Profinite methods in finite semigroup theory, in Proc. Int. Conf. on Math. Logic, Novosibirsk State Univ., Novosibirsk, 2002, 3-28

77. (with A. Bulatov and P. Jeavons) Finite semigroups imposing tractable constraints, in G. M. S. Gomes, J.- É. Pin and P. V. Silva (eds.), Semigroups, Algorithms, Automata and Languages, World Scientific, Singapore, 2002, 313-329

76. Semimodular and arguesian semigroup varieties: identities, Izvestija Ural'skogo Universiteta. Matematika i Mekhanika (2002) no.22, 44-63 [Russian].

75. Gyorgy Pollák's work on the theory of semigroup varieties: its significance and its influence so far, Acta Sci. Math. Szeged (2002) 68, no.3-4, 875-894. (

The paper was initially published in Acta Sci. Math. Szeged (2002) 68, no.1, 9-28 but since the whole issue suffered from a typesetting mistake, the most affected papers including this one were reprinted.)74. Some open problems concerning relatively free and free profinite semigroups, Semigroup Forum (2002) 64, no.2, 224-235.

73. (with D. S. Ananichev) Collapsing words vs. synchronizing words, in W. Kuich, G. Rozenberg, A. Salomaa (eds.), Developments in Language Theory [Lect. Notes Comput. Sci. 2295], Springer, Berlin-Heidelberg-N.Y., 2002, 166-174.

72. Decidability of finite quasivarieties generated by certain transformation semigroups, Algebra Universalis (2001) 46, no.1, 97-103.

71. The finite basis problem for finite semigroups, Math. Japonica (2001), 53, no.1, 171-199.

70. (with J. Almeida and P. M. Higgins) The gap between partial and full: an addendum, Int. J. Algebra and Computation (2001), 11, no.1, 131-135.

69. (with B. M. Vernikov) Commuting fully invariant congruences on free semigroups, Contrib. Gen. Algebra (2000), 12, 391-417.

68."Forbidden divisor" characterizations of epigroups with certain properties of group elements, "Algebraic Systems, Formal Languages and Computations" (RIMS Kokyuroku 1166), Research Institute for Mathematical Sciences, Kyoto University, 2000, 226-234.

67. (with B. M. Vernikov) The structure of lattices of nil-semigroup varieties, Izvestija Ural'skogo Universiteta. Matematika i Mekhanika (2000) no.18, 34-52 [Russian].

66. The finite basis problem for finite semigroups: a survey, in P. Smith, E. Giraldes, P. Martins (eds.), Semigroups, World Scientific, Singapore, 2000, 244-279.

65. Conditional equations for pseudovarieties, in C. L. Nehaniv, M. Ito (eds.) Algebraic Engineering, World Scientific, Singapore, 1999, 376-389.

64. (with O. B. Paison and M. V. Sapir) Finite separability in varieties of associative rings, Algebra i logika (1999) 38, no.2, 201-227 [Russian; English translation Algebra and Logic (1999) 38, no.2, 107-120].

63. (with G. V. Tanana) Varieties of adjoined regular rings. Izvestija Ural'skogo Universiteta. Matematika i Mekhanika (1999) no.14, 23-28 [Russian].

62. (with J. Almeida) The gap between partial and full, Int. J. Algebra and Computation (1998) 8, no.3, 399-430.

61. (with D. S. Ananichev) Varieties of soluble Lie rings of finite width, Mat. Zametki (1998) 63, no.5, 643-650 [Russian; English translation Math. Notes (1998) 63, no.5, 569-574].

60. (with V. B. Repnitski ) The finite basis problem for the pseudovariety O, Proc. Royal Soc. Edinburgh (1998) 128A, 661-669.

59. (with B. M. Vernikov) Lattices of nilpotent semigroup varieties. II, Izvestija Ural'skogo Universiteta. Matematika i Mekhanika (1998) no.10, 13-33 [Russian].

58. The finite basis problem for the pseudovariety PO, in J. M. Howie and N. Ruskuc (eds.), Semigroups and Applications, World Scientific, Singapore, 1998, 239-257

57. (with E. Graczynska and R. Pöschel) Solid pseudovarieties, in General Algebra and Applications to Discrete Mathematics, Shaker Verlag, Aachen, 1997, 93-110.

56. (with B. M. Vernikov) Permutability of fully invariant congruences on relatively free semigroups, Acta Sci. Math. (Szeged) (1997) 63, no.3-4, 437-461.

55. (with P. G. Trotter) The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups, Semigroup Forum (1996) 52, no.1, 83-91.

54. Covers in the lattices of semigroup varieties and pseudovarieties, in J. Almeida, G. M. S. Gomes, P. V. Silva (eds.), Semigroups, Automata and Languages, World Scientific, Singapore, 1996, 263-280.

53. (with F. Pastijn) Minimal non-cryptic e-varieties of regular semigroups, J. Algebra (1996) 184, no.3, 881-896.

52. (with A. V. Tishchenko) A characterization of semigroup varieties of finite index in the "forbidden divizors" language, Izv. VUZ. Matematika (1995) no.1, 91-99 [Russian; English translation Russ. Math., Izv. VUZ (1995) 39, no.1, 84-92].

51. (with A. S. Vernitski) A proof and a generalisation of Higgins's division theorem for semigroups of order-preserving mappings, Izv. VUZ. Matematika (1995) no.1, 38-44 [Russian; English translation Russ. Math., Izv. VUZ (1995) 39, no.1, 34-39].

50. (with N. N. Silkin) Associatively amalgamatable varieties of rings, Mat. Zametki (1995) 57, no.2, 203-213 [Russian; English translation Math. Notes (1995) 57, no.1-2, 141-147].

49. On a class of semigroup pseudovarieties without finite pseudoidentity basis, Int. J. Algebra and Computation (1995) 5, no.2, 127-135.

48. (with M. V. Sapir) On the join of semigroup varieties with the variety of commutative semigroups, Proc. Amer. Math. Soc. (1994) 120, no.2, 345-348.

47. Young diagrams and the structure of the lattice of overcommutative semigroup varieties, in Transformation Semigroups. Proc. Int. Conf. held at the Univ. of Essex, Colchester, 1994, 99-110.

46. (with R. Pöschel, M. V. Sapir, N. Sauer, and M. Stone) Identities in full transformation semigroups, Algebra Universalis (1994) 31, no.4, 580-588.

45. Varieties of associative rings whose critical rings are basic, Sib. Mat. Zh. (1993) 34, no.1, 38-46 [Russian; English translation Siberian Math. J. (1993) 34, no.1, 30-36].

44. (with B. M. Vernikov) Structure of lattices of nilpotent semigroup varieties, in Semigroups: Algebraic Theory and Applications to Formal Languages and Codes, World Scientific, Singapore, 1993, 297-299

43. Semigroup varieties with modular subvariety lattice. III, Izv. VUZ. Matematika (1992) no.8, 21-29 [Russian; English translation Russ. Math., Izv. VUZ (1992) 36, no.8, 18-25].

42. Semigroup varieties with modular subvariety lattice. II, Izv. VUZ. Matematika (1992) no.7, 3-8 [Russian; English translation Russ. Math., Izv. VUZ (1992) 36, no.7, 1-6].

41. Semigroup varieties with modular subvariety lattices, Dokl. RAN (1992) 326, no.3, 409-413 [Russian; English translation Russ. Acad. Sci. Dokl. Math. (1993) 46, no.2, 274-278].

40. Semigroup varieties with commuting fully invariant congruences on free objects, Contemp. Math. (1992) 131, part 3, 295-316. (

The "if" part of the main theorem is wrong. The error is discussed and corrected in [56].)39. Commutative semigroup varieties with distributive subvariety lattices, Contrib. Gen. Algebra (1991) 7, 351-359.

38. (with T. A. Ershova) The lattice of varieties of semigroups with completely regular square, in Monash Conf. on Semigroup Theory in Honour of G B Preston, World Scientific, Singapore, 1991, 306-322.

37. (with B. M. Vernikov) Commutative semigroup varieties with modular subvariety lattices, in Monoids and Semigroups with Applications. Proc. Berkeley Workshop in Monoids, World Scientific, Singapore, 1991, 233-253.

36. A general finite basis condition for systems of semigroup identities, Semigroup Forum (1990) 41, no.2, 183-194.

35. (with A. V. Kelarev) Separation of the radical in ring varieties. II. Acta Sci. Math. (Szeged) (1990) 54, no.1-2, 53-56.

34. (with S. Vovsi) On multilinear identities of group representations, Comm. Algebra (1990) 18, no.2, 389-401.

33. On finite basedness of semigroup varieties, Mat. Zametki (1989) 45, no.3, 12-23 [Russian; English translation Math. Notes (1989) 45, no.3, 187-194].

32. Semigroup varieties with modular subvariety lattice, Izv. VUZ. Matematika (1989) no.6, 51-60 [Russian; English translation Soviet Math. Izv. VUZ (1989) 33, no.6, 48-58]. (

There is an inaccuracy in the formulation of the condition (b) of Theorem 1. This inaccuracy is discussed and corrected in [42].)31. Ring varieties determined by their subvariety lattices, Mat. Zapiski UrGU (1989) 14, no.4, 37-55 [Russian].

30. (with M. V. Sapir) HFB property and structure of semigroups, Contrib. Gen. Algebra (1988) 6, 303-310.

29. (with B. M. Vernikov) Lattices of nilpotent semigroup varieties, Mat. Zapiski UrGU (1988) 14, no.3, 53-65 [Russian].

28. Identities in the lattices of ring varieties, Algebra Universalis (1986) 23, no.1, 32-43.

27. (with A. V. Kelarev) Varieties and bands of associative rings, Izv. VUZ. Matematika (1986) no.9, 16-23 [Russian; English translation Soviet Math. Izv. VUZ (1986) 30, 21-33].

26. On the identity bases of Brandt semigroups, Mat. Zapiski UrGU (1985) 14, no.1, 38-42 [Russian]. (There is a lacuna in the proof of the main result. It it discussed and fixed in [149])

25. (with Gy. Pollák) On almost simple semigroup identities, in Semigroups. North Holland, Amsterdam, 1985, 287-323.

24. (with L. N. Shevrin) Identities of semigroups, Izv. VUZ. Matematika (1985) no.11, 3-47 [Russian; English translation Soviet Math Izv. VUZ (1985) 29, no.11, 1-64].

23. Pronilpotent varieties of universal algebras, Mat. Zapiski UrGU (1984) 13, no.4, 39-41 [Russian].

22. Finite basis theorem for systems of semigroup identities, Semigroup Forum (1984) 28, no.1-3, 93-99.

21. Distributivity of certain lattices of varieties of associative rings, Sib. Mat. Zh. (1984) 25, no.6, 23-30 [Russian; English translation Siberian Math. J. (1984) 25, no.6, 849-855].

20. On the join of varieties, Simon Stevin (1984) 58, no.4, 311-317.

19. (with B. M. Vernikov) Dualisms in lattices of varieties of associative rings, Izv. VUZ. Matematika (1984) no.9, 66-69 [Russian; English translation Soviet Math. Izv. VUZ (1984) 28, no.9, 90-94]. Correction ibid. (1986) no.4, 86 [Russian; Engl. translation Soviet Math. Izv. VUZ (1986) 30, no.4, 111].

18. (with B. M. Vernikov) Dualisms in lattices of varieties of associative rings, Mat. Zapiski UrGU (1984) 13, no.4, 11-38 [Russian]. Correction ibid. (1987) 14, no.2, 141-142 [Russian].

17. On the lower floors of the lattice of associative ring varieties, Mat. Zapiski UrGU (1983) 13, no.3, 25-36 [Russian].

16. Varieties of associative rings with the property of embeddability of amalgams, Mat. Zametki (1983) 33, no.1, 3-13 [Russian; English translation Math. Notes (1983) 33, no.1, 3-7].

15. Varieties of associative rings closed under ideal sums, Comment. Math. Univ. Carolinae (1983) 24, no.1, 101-103.

14. On the join of semigroup varieties, Contrib. Gen. Algebra (1983) 2, 365-373.

13. Separation of the radical in ring varieties, Acta Sci. Math. (Szeged) (1983) 46, no.1, 73-75.

12. An example of a limit variety of semigroups, Semigroup Forum (1982) 24, no.4, 319-326.

11. On finite basedness of ring varieties of a finite index. III, Mat. Zapiski UrGU (1982) 13, no.1, 3-6 [Russian].

10. (with A. G. Gein) Identities in almost nilpotent Lie rings, Mat. Sbornik (1982) 118, no.1, 132-142 [Russian; English translation Math. USSR, Sb. (1983) 46, 133-142].

9. (with B. M. Vernikov) Complemented lattices of varieties and quasivarieties, Izv. VUZ. Matematika (1982) no.11, 17-20 [Russian; English translation Soviet Math. Izv. VUZ (1982) 26, 19-24].

8. Lattices of varieties of nilpotent rings, Mat. Zapiski UrGU (1981) 12, no.3, 19-34 [Russian].

7. Finiteness of a basis of identities of some associative rings, Sib. Mat. Zh. (1981) 22, no.4, 79-87 [Russian; English translation Siberian Math. J. (1982) 22, no.4, 545-551].

6. (with B. M. Vernikov) Finite basedness of some varieties satisfying a permutation identity, Mat. Zapiski UrGU (1980) 12, no.2, 3-23 [Russian].

5. Periodic varieties of associative rings, Izv. VUZ Matematika (1979) no.8, 3-13 [Russian; Engl. translation Soviet Math. Izv. VUZ (1979) 23, no.1, 1-12].

4. (with B. M. Vernikov) Almost chain varieties of alternative rings, Mat. Zapiski UrGU (1979) 11, no.3, 22-39 [Russian]. Correction ibid. (1983) 13, no.3, 158 [Russian].

3. Lattices of varieties of algebras, Mat. Sbornik (1979) 109, no.1, 60-79 [Russian; English translation Math. USSR, Sb. (1980) 37, no.1, 53-69].

2. On finite basedness of ring varieties of a finite index. II, Mat. Zapiski UrGU (1979) 11, no.3, 40-43 [Russian].

1. On finite basedness of ring varieties of a finite index, Mat. Zapiski UrGU (1977) 10, no.3, 26-32 [Russian].

Identities in Lattices of Semigroup Varieties, Doctor of Physical and Mathematical Sciences Thesis, defended in May 1994 at St Petersburg State University [Russian, English translation]

Lattices of Ring Varieties, Candidate of Physical and Mathematical Sciences Thesis, defended in March 1980 at the Mathematics Institute of the Moldavian Academy of Sciences [Russian]

(with V. Diekert) Developments in Language Theory. 26th International Conference, DLT 2022, Tampa, FL, USA, May 9-13, 2022 Proceedings. [Lect. Notes Comp. Sci. 13257], Springer, Cham, 2022.

(with P. G. Romeo and A. R. Rajan) Semigroups, Categories, and Partial Algebras [Springer Proc. Math. & Statistics 345], Springer Singapore, Singapore, 2021.

(with V. Kabanov, A. Kondrat'ev, E. Konstantinova, N.Maslova) Groups and Graphs, Metrics and Manifolds, 2017: Abstracts of the International Conference and PhD-Master Summer School on Groups and Graphs, Metrics and Manifolds, Ural Federal University, Yekaterinburg, 2017.

(with A. M. Shur) Developments in Language Theory. 18th International Conference, DLT 2014, Ekaterinburg, Russia, August 2014. Proceedings. [Lect. Notes Comp. Sci. 8633], Springer-Verlag, Berlin-Heidelberg-N.Y., 2014.

(with V. Diekert, A. Voronkov) Computer Science - Theory and Applications. 2nd International Symposium on Computer Science in Russia, CSR 2007. Ekaterinburg, Russia, September 2007, Proceedings. [Lect. Notes Comp. Sci. 4649], Springer-Verlag, Berlin-Heidelberg-N.Y., 2007.

(with L. N. Shevrin, V. A. Baranskii, Ju. M. Vazhenin, A. G. Gein, A. P. Zamjatin, A. Ja. Ovsjannikov, A. N. Petrov, N. F. Sesekin) Problem book in general algebra and discrete mathematics, Ural University Publishing, Ekaterinburg, 2003, 140 pp. [Russian]

(with V. V. Rasin, D. S. Ananichev, A. G. Gein, S.P. Khomenko, A. M. Shur, V.P. Ivanova) Entrance exams in mathematics in Ural State University in 2003. Ural University Publishing, Ekaterinburg, 2003, 44 pp. [Russian]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Teacher's companion for the textbook Mathematics 5. Education Publishing, Moscow, 2003, 160 pp. [Russian]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Exercise Notebook accompanying the textbook Mathematics 6. Education Publishing, Moscow, 2002 (2nd revised and expanded edition), 144pp. [Russian]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Exercise Notebook accompanying the textbook Mathematics 5. Education Publishing, Moscow, 2002 (2nd revised and expanded edition), 144pp. [Russian]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Mathematics 6 (A textbook for secondary schools.) Education Publishing, Moscow, 2001 (4th revised and expanded edition), 288 pp. [Russian]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Mathematics 5 (A textbook for secondary schools.) Education Publishing, Moscow, 2000 (4th revised and expanded edition), 368pp. [Russian]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Exercise Notebook accompanying the textbook Mathematics 6. Education Publishing, Moscow, 1997, 80pp. [Russian]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Exercise Notebook accompanying the textbook Mathematics 5. Education Publishing, Moscow, 1996, 80pp. [Russian]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Mathematics 6 (A textbook for secondary schools.) Education Publishing, Moscow, 1992 (2nd edition 1995, 3rd edition 1997), 224pp. [Russian; Belorussian translation by People Education Publishing, Minsk, 1995, 224pp.]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Mathematics 5 (A textbook for secondary schools.) Education Publishing, Moscow, 1992 (2nd edition 1994, 3rd edition 1996), 320pp. [Russian; Belorussian translation by People Education Publishing, Minsk, 1994, 320pp.]

(with L. N. Shevrin, A. G. Gein, I. O. Koryakov) Mathematics 5-6. (A textbook for secondary schools.) Education Publishing, Moscow, 1989, 496pp. [Russian]

The Sverdlovsk notebook. Unsolved problems of the semigroup theory. 3rd issue. Edited by V. A. Baranski , M. V. Volkov, E. A. Golubov, L. N. Shevrin. Ural State University, Sverdlovsk, 1989, 40pp. [Russian]

III All-Union Symposium on the theory of semigroups. Abstracts of talks, Edited by V. A. Baranski , Ju. M. Vazhenin, M. V. Volkov, E. A. Golubov, A. P. Zamjatin, E. V. Sukhanov, L. N. Shevrin. Ural State University, Sverdlovsk, 1988, 112pp. [Russian]

G.Paun, G. Rozenberg and A. Salomaa, DNA Computing. New Computing Paradigms, translated from English by D. S. Ananichev, O. B. Finogenova, I. S. Kisileva, edited by M. V.Volkov. Mir, Moscow, 2004, 528 pp. [Russian]

*Other scientific
publications:*

16. (with E. A. Bondar) Completely reachable automata: an interplay between semigroups, automata, and trees, in K. Reinhardt, L. Staiger, R. Winter (eds.), Theorietage 2018. 76. Workshop über Algorithmen und Komplexität. 28. Theorietag Automaten und Formale Sprachen. Proceedings [Universität Halle-Wittenberg, Technical Report No. 18-1], Universität Halle-Wittenberg. 2018, 33-36.

15. (with E. A. Bondar) A characterization of completely reachable automata, in H. Fernau (ed.), Theorietag 2017. Automaten und Formale Sprachen [Technical Reports Mathematics/Computer Science, No. 17-1], University of Trier, 2017, 10-13.

14. (with K. Auinger and I. Dolinka) Matrix identities involving multiplication and transposition, in J. Karhumäki, A. Saarela (eds.), Proceedings of the Finnish Mathematical Days 2016 [TUCS Lect. Notes, No. 25], Turku Centre for Computer Science, 2016, 15-23.

13. The Finite Basis Problem, Section 4.5 in M. V. Sapir, Combinatorial Algebra: Syntax and Semantic, Springer, 2014, 187-194.

12. Subshifts and automata. The Road Coloring Problem, Section 3.9 in M. V. Sapir, Combinatorial Algebra: Syntax and Semantic, Springer, 2014, 137-152.

11. A remarkable scientist, a remarkable friend, in Outorga do Titulo de Professor Emerito a Imre Simon, Universidade de Sao Paulo, 2009, 113-115.

10. (with M. O. Asanov and A. S. Lakhtin) Master programs at the Department of Mathematics and Mechanics of Ural State University, in Innovation Experience in Education and Science, Ural Publishers, 2005, 83-87 [Russian].

9. Asynchronous automaton, in V. Yu. Kozlov (ed.) Discrete Mathematics. Encyclopedia, Russian Encyclopedia, 2004, 27 [Russian].

8. Trace theory, in V. Yu. Kozlov (ed.) Discrete Mathematics. Encyclopedia, Russian Encyclopedia, 2004, 247-248 [Russian].

7. (with L. N. Shevrin) Pseudovarieties of universal algebras, in V. Yu. Kozlov (ed.) Discrete Mathematics. Encyclopedia, Russian Encyclopedia, 2004, 277-278 [Russian].

6. (with L. N. Shevrin) Varieties and quasivarieties, Section G.5 in G. Pilz, A. V. Mikhalev (eds.), The Concise Handbook of Algebra, Kluwer Academic Publishers, 2002, 465-469.

5. (with L. N. Shevrin) Varieties of semigroups, Section A.15 in G. Pilz, A. V. Mikhalev (eds.), The Concise Handbook of Algebra, Kluwer Academic Publishers, 2002, 58-62.

4. Pal Erdös: an unusual life and incredible mathematics, MIF (1998/99) no.2, 4-11 [Russian].

3. The finite basis problem, MIF (1996/97) no.2, 4-15; 79-81 [Russian].

2. (with L. N. Shevrin, A. G. Gein, I. O. Koryakov) On the book "Mathematics 5-6", Matematika v shkole (1989) no.2, 78-87; no.3, 87-95 [Russian].

1. (with N. N. Silkin) Who should be sent to Mars? Quant (1988) no.8, 51-57; no.9, 75-77 [Russian].