Characteristic sequences of non-associative algebras (with D.K. Kudryavtsev) Communications in Algebra, 48(4), 2000, 1713-1725. - Majorization for (0,1)-matrices (with G. Dahl and P. Shteyner) Linear Algebra and Its Applications, 585, 2020, 147-163

Orthogonality for (0,-1) tropical normal matrices (with B. Bakhadly and M. J. de la Puente) Special Matrices, 8, 2020, 40-60 - Permanent Polya problem for additive surjective maps (with I.A. Spiridonov) Linear Algebra and Its Applications, 599, 2020, 140-155

Upper bounds for the length of non-associative algebras (with D.K. Kudryavtsev) Journal of Algebra, 544, 2020, 483-497 - Linear transformtions preserving majorizations for matrix tuples (with P. Shteyner) Vestnik St.Petersburg University, Mathematics, 53(2), 2020, 136144

2-words, their graphs and matrices (with E.M. Kreines and N.V. Ostroukhova) Zapiski Nauch. Sem. POMI, 482, 2019, 45-72 - Graph characterization of fully indecomposable nonconvertible (0,1)-matrices with minimal number of ones (with M. Budrevich, G. Dolinar Gregor, B. Kuzma) Ars Mathematica Contemporanea, 17(1), 2019, 141-151

Krauter conjecture on permanents is true (with M.V. Budrevich) Journal of Combinatorial Theory - Series A, 162, 2019, 306-343 - Length realizability for pairs of quasi-commuting matrices (with O. Markova, V. Mehrmann) Linear Algebra and Its Applications, 568, 2019, 135-154

More on geometry of Krein space C-numerical range (with R. Lemos and G. Soares) Applied Mathematics and Computation, 352, 2019, 258-269 - - Double centralizing theorem with respect to q-commutativity relation (with Gregor Dolinar, Bojan Kuzma, Olga Markova) Journal of Algebra and its Applications, 18(1), 2019, 1-15

- Additive maps preserving scrambling index are bijective (with A.M. Maksaev) Acta Mathematica Hungarica, 84(1-2), 2018, 19-38 - - Majorization for matrix classes (with Geir Dahl and Pavel Shteyner) Linear Algebra and Its Applications, 555, 2018, 201-221

- Extremal generalized centralizers in matrix algebras (with G. Dolinar, B. Kuzma, O. Markova) Communications in Algebra, 46(7), 2018, 3147-3154 - - A resolution of Paz’s conjecture in the presence of a nonderogatory matrix (with T. Laffey, O. Markova, H. Smigoc) Linear Algebra and Its Applications, 543, 2018 234-250 ˇ

- On Hartwig–Nambooripad orders (with X. Mary, P. Shteyner) Semigroup Forum (2018). https://doi.org/10.1007/s00233-018-9940-7 - - Linear isomorphisms preserving Green’s relations for matrices over anti-negative semifields (with Marianne Johnson, Mark Kambites) Linear Algebra and Its Applications, 545, 2018, 1-14

- Monotone linear maps of matrices over semirings (with E.M. Kreines, Q.-W. Wang) Journal of Mathematical Sciences (New York), 233(5), 2018, 675-686 - - Maps preserving scrambling index (with Maksaev A.M.) Linear and Multilinear Algebra, 69(4), 2018, 840-851 - - Converting immanants on singular symmetric matrices (with Duffner A.) Lobachevskii Journal of Mathematics, 38(4), 2017, 630-636

- The lengths of the quaternion and octonion algebras (with Kudryavtsev D.K.) Journal of Mathematical Sciences (New York), 224(6), 2017, 826-833 - - Preserving 0 and 1 values of the scrambling index (with Maksaev A.M.) Proceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics: Organized in Turku on 16.-19.5.2017, Turku Center for Computer Science, Turku. 57-59

- Lower bound for Polya problem on permanent (with Mikhail V. Budrevich, Gregor Dolinar, Bojan Kuzma) International Journal of Algebra and Computation, 26(6), 2016, 1237-1255 - - Lengths of quasi-commutative pairs of matrices (with Markova O.V., Mehrmann V.) Linear Algebra and Its Applications, 498, 2016, 450-470

26. Rank functions of tropical matrices (with Ya. Shitov) Linear Algebra and its Applications, 498, 2016, 326-348 - - On the C-determinantal range for special classes of matrices (with R. Lemos and G. Soares) Applied Mathematics and Computation (New York), 275, 2016, 86-94.

- The realizability problem for the values of the length function of quasi-commuting matrix pairs (with Markova O.V.) Journal of Mathematical Sciences (New York), 216(6), 2016, 761-769 - - Continuous monotone matrix maps for orders induced by the group inverse (with Efimov M.A.) Journal of Mathematical Inequalities, 10(1), 2016, 123-133

- Lengths of quasi-commutative pairs of matrices (with Markova O.V., Mehrmann V.) Linear Algebra and Its Applications, 498, 2016, 450-470 - - New matrix partial order based on spectrally orthogonal matrix decomposition (with A. Herrero, N. Thome) Linear and Multilinear Algebra, 64(3), 2016, 362-374

- On the divisibility of permanents for (+/-1)-matrices (with Budrevich M.V., Taranin K.A.) Journal of Mathematical Sciences (New York), 216(6), 2016, 738-745 - - The arctic rank of a Boolean matrix (with Beasley L.B., Shitov Ya. N.) Journal of Algebra, 433, 2015, 168-182

- Maps on operators strongly preserving sharp order (with Efimov M.A.) Operators and Matrices, 9(3), 2015, 711-731 - - Graphs Defined by Orthogonality (with B.R. Bakhadly, O.V. Markova) Journal of Mathematical Sciences (New York), 207(5), 2015, 698-717

- Characterizing monotone maps on matrices and operators, Classical and Functional Analisys, Ser. 2-3, Transilvania University Press Brasov, Romania, 2015, 5-16

- Immanant conversion on symmetric matrices (with C. Purifica¸c˜ao, A. Duffner) Special Matrices, 2(1), 2014, 1-10. - - Guterman A. E., On the Polya conversion problem for permanents and determinants Journal of Mathematical Sciences, 187(6), 2014, 782-786.

- Monotone maps on diagonalizable matrices (with M.A. Efimov), Mathematical Inequalities and Applications, 17(4), 2014, 1441-1452.

- Tropical Cramer determinants revisited (with M. Akian, S. Gaubert) American Mathematical Society, Contemporary Mathematics, 616, Amer. Math. Soc., Providence, RI, 2014, 1-45.

- The algebra of semi-magic matrices and its length (with O.V. Markova, S.D. Sochnev) Zapiski POMI, 419, 2013, 52-77. - - Commuting graphs and extremal centralizers (with G. Dolinar, B. Kuzma, P. Oblak), Ars Mathematica Contemporanea, 7(2), 2014, 453-459. - - Commutativity preservers via matrix centralizers (with G. Dolinar, B. Kuzma, P. Oblak), Publicationes Mathematicae Debrecen, 84(3-4) (2014), 439-450. - - Extremal matrix centralizers (with G. Dolinar, B. Kuzma, P. Oblak), Linear Algebra and its Applications, 438(7), 2013, 2904-2910 - - Extremal case in Marcus-Oliveira conjecture and beyond (with R. Lemos, and G. Soares), Linear and Multilinear Algebra, 61(9), 2013, 1206-1222. - - Permanent versus determinant over a finite field (with G. Dolinar, B. Kuzma, M. Orel), Journal of Mathematical Sciences (New-York), 193(3), 2013, 404-412. - - Monotone maps on index one matrices (with M.A. Efimov), Zapiski POMI, 405, 2012, 67-96. - - On the Gibson bounds over finite fields (with M.V. Budrevich), Serdica Math. J. 2012, 38, - 395-416 - - Automorphisms of B(H) with respect to the left-star and the right-star partial order (with G. - Dolinar and J. Marovt), Mathematical Inequalities and Applications, 17(2), 2014, 573-589. - - Students Olympiads in Algebra at the Department of Mathematics and Mechanics, MSU - (with I.V. Arzhantsev, V.V. Batyrev, E.I. Bunina, E.S. Golod, M.V. Zaicev, A.I. Zobnin, A.A. Klyachko, V.T. Markov, A.A. Nechaev, A.Yu. Olshanskii, E.A. Porshnev, Yu.G. - Prokhorov), Moscow, MCCME, 2012, pp. 72. - - Permanent has less zeros than determinant over finite fields (with M. Budrevich), American - Mathematical Society, Contemporary Mathematics, 579, 2012, 33-42 - - On the Polya permanent problem over finite fields (with G. Dolinar, B. Kuzma, M. Orel), European Journal of Combinatorics, 32, 2011, 116-132. - - On Gibson barrier for Polya problem (with G. Dolinar, B. Kuzma), Fundamental and Applied Mathematics, 16(8), 2010, 73-86 - - Operators preserving primitivity for matrix pairs (with L.B. Beasley), Matrix Methods: Theory, Algorithms, Applications, Word Scientific Publishing, 2010, 2-20 - - Additive Frobenius endomorphisms for Sylvester and related bounds (with Graca Soares), Contributions to General Algebra, Verlag Johannes Heyn, 19, 2010, 91-102 - - The correspondence between tropical convexity and mean payoff games (with Marianne Akian, Stephane Gaubert), Mathematical Theory of Networks and Systems, 2010, 1295-1302 - - On the independence numbers of distance graphs with vertices at $\{-1,0,1\}\sp n$: bounds, conjectures and applications to the problems by Nelson-Erdos-Hadviger and Borsuk. (with V.K. Lyubimov, A.M. Raigorodskii, S.A. Usachev), Contemporary Mathematics and Applications, 65, 2009, 82-100. - - Frobenius endomorphisms of matrix spaces and their applications, Operator Theory and Operator Algebras, 2009, 33-42. - - On the independence numbers of distance graphs with vertices at $\{-1,0,1\}\sp n$. ( with V.K. Lyubimov, A.M. Raigorodskii, S.A. Usachev), Mat. Zametki, 86, (2009), no. 5, 794–796. - - Frobenius Endomorphisms on matrix spaces (with A.V. Mikhalev), Contemporary Problems of Mathematics and Mechanics, 4(3), 2009, 71-105. - - Matrix ranks and linear independence over tropical semirings (with M. Akian, S. Gaubert), American Mathematical Society, Contemporary Mathematics, 495, 2009, 1-33. - - Preserving zeros of a polynomial (with B. Kuzma), Communications in Algebra, 37(11), 2009, 3801-3827. - - Matrix invariants over semirings, Handbook of Algebra, Elseiver, 6, 2009, 3-33. - - The characterization of operators preserving primitivity for matrix k-tuples (with L. B. Beasley), Linear Algebra and its Applications, 430, 2009, 1762-1777. - - Commutative matrix subalgebras and length function (with O. V. Markova), Linear Algebra and its Applications, 430, 2009, 1790-1805. - - Maps preserving zeros of matrix polynomials (with B. Kuzma), Doklady of Russian Academy of Sciences, Mathematics, 427(3), 2009, 300-302. - - Preserving regular tournaments and term rank-1 (with L.B. Beasley, D. Brown), Linear Algebra and its Applications, 431, 2009, 926-936. - - Operators preserving primitivity for matrix pairs (with L. B. Beasley), Matrix Methods: Theory, Algorithms, Applications, Word Scientific Publishing, 2008, 2-20. - - On linear operators preserving the set of positive polynomials (with B. Shapiro), Journal of Fixed Point Theory and Applications, 3 (2), 2008, 411-429. - - Characterization of transformations strongly preserving zeros of matrix polynomials (with B. Kuzma), Uspehi Mat. Nauk, 63(5), 2008, 184-185. [in Russian] - - Rank and determinant functions for semirings, London Mathematical Society Lecture Notes, 347, 2007, 1-33. - - Transformations preserving matrix invariants over semirings, Idempotent and tropical mathematics and problems of mathematical physics, Moscow, MCCME, 1, 2007, 84-90 - - Monotone additive transformations on matrices, Mat. Zametki, 81(5), 2007, 681–692. - - Monotone matrix mappings defined by the group inverse and simultaneous diagonalizability (with I. I. Bogdanov), Mat. Sbornik, 198(1), 2007, 3-20. - - Idempotent matrices and majorisation (with L. B. Beasley, K.-T. Kang, S.-Z. Song), Fundamental and Applied Mathematics, 13(1), 2007, 11-29. - - Frobenius and Dieudonne theorems over semirings (with L. B. Beasley, S.-G. Lee, S.-Z. Song), Linear and Multilinear Algebra, 55(1), 2007, 19-34 - - Linear preservers of extremes of rank inequalities over semirings: the row and column ranks (with L. B. Beasley, Y.-B. Jun, S.-Z. Song), Linear Algebra Appl., 413, 2006, 495-509 - - Rank-permutable additive mappings (with A. A. Alieva, B. Kuzma), Linear Algebra Appl., 414, 2006, 607-616 - - Linear preservers for Sylvester and Frobenius bounds on matrix rank (with L. B. Beasley, C. L. Neal), Rocky Mountain Journal of Mathematics, 86(1), 2006, 67-80 - - Linear preservers of zeros of matrix polynomials (with L. B. Beasley, S.-G. Lee, S.-Z. Song), Linear Algebra and its Applications, 2005, 401, 325-340 - - Monotone linear transformations on matrices are invertible (with A. A. Alieva), Communications in Algebra, 33, 2005, 3335-3352 - - Rank inequalities over semirings (with L. B. Beasley), Journal of Korean Math. Soc., 42(2), 2005, 223-241 - - Factor rank for nonnegative matrices (with O. A. Vaysman), Chebyshevskii Sbornik, 6(4), 2005, 64-67 [in Russian] - - Linear preservers of extremes of rank inequalities over semirings: term rank and zero-term rank (with L. B. Beasley and S.-C. Yi), Fundamental and Applied Mathematics, 10(2), 2004, 3-21 [in Russian] - - Linear preservers of rank permutability (with A. A. Alieva), Linear Algebra and its Applications, 384, 2004, 97-108 - - Linear Transformations Preserving the Grassmannian over M_n(Z+) (with L. B. Beasley, S.-G. Lee, S.-Z. Song), Linear Algebra and its Applications, 393, 2004, 39-46 - - Linear Transformations Preserving Matrix Invariants (with A.V. Mikhalev), Mathematics. Mechanics. Informatics. 10 years RFFI. Fizmatlit, 2004, 501(3),165-186 [in Russian] - - LP-problems for rank inequalities over semirings: factorization rank (with L.B. Beasley), Sovrem. Mat. Prilozh. Algebra, 13, 2004, 53-70 [in Russian] - - Rank permutability and additive operators preserving some rank product conditions (with A. A. Alieva), Fundamental and Applied Mathematics, 10(4), 2004, 3-14 [in Russian] - - Linear transformations preserving rank-commutativity (with A. A. Alieva), Bull. of the Moscow State University. Ser. 1. Mathematics. Mechanics, 6, 2003, 11-17 [in Russian] - - Transformations of non-negative integer matrices preserving the determinant, Uspehi Mat. Nauk, 58(6), 2003 147-148 [in Russian] - - Monotone Matrix Maps Preserve Non-Maximal Rank, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, 2003, 311-328 - - General Algebra and Linear Transformations Preserving Matrix Invariants (with A.V. Mikhalev), Fundamental and Applied Mathematics, 9(1), 2003, 83-101 [in Russian] - - Linear transformations that preserve the Dieudonne determinant over an arbitrary division ring, Uspehi Mat. Nauk, 57(4), 2002, 171-172 [in Russian] - - Identities of near-triangular matrices, Matem. Sbornik, 192(6), 2001, 3-15 - - Linear preservers for matrix inequalities and partial orderings, Linear Algebra and its Applications, 331, 2001, 75-87 - - Frobenius type theorems in the noncommutative case, Linear and Multilinear Algebra, 48(4), 2001, 293-312 - - Linear preservers for Drazin star partial order, Communications in Algebra, 29(9), 2001, 3905-3917 - - Linear transformations, preserving super-rank, Mathematical Methods and Applications, MSSU, 8, 2001, 100-104 [in Russian] - - Graded local rings, Fundamental and Applied Mathematics, 6(3), 2000, 753-756 [in Russian] - - Some general techniques on Linear Preserver Problems (with C.-K. Li, P. Semrl), Linear Algebra and Applications, 315, 2000, 61-81 - - Singularity preservers over local domains, Journal of Mathematical Sciences, 102(6), 2000, 4591-4597. - - On the Growth of Identities (with A.Regev), Algebra. Berlin, New York: Walter de Gruyter, 2000, 319-331 - - On determinant preservers over noncommutative Principal Ideal Domains (with A. V. Mikhalev), Lie Algebras, Rings, and Related Topics, Hong Kong: Springer-Verlag, 2000, 49-60 - - Ph. Hall type theorems for modules (with E. Kreines), Universal Algebra and its Applications, Volgograd, 2000, 60-72 - - A note on linear preservers of a certain matrix partial order, Formal Power Series and Algebraic Combinatorics, Berlin: Shpringer-Verlag, 2000, 441-446 - - On the applications of Model Theory for the classifications of linear transformations preserving matrix invariants, Mathematical Methods and Applications, MSSU, 7, 2000, 53-57 [in Russian] - - P. Hall’s theorem on transversals for modules (with E. Kreines), Fundamental and Applied Mathematics, 5(1), 1999, 119-130 [in Russian] - - Identities and codimensions of a certain subalgebra of triangular matrix algebra, Mathematical Methods and Applications, MSSU, 6, 1999, 79-82 [in Russian] - - Linear transformations preserving Adjamagbo determinant, Mathematical Methods and Applications, MSSU, 6, 1999, 67-72 [in Russian] - - Frobenius type results for matrices over the skew-fields (with E. M. Kreines, A. V. Mikhalev), Mathematical Methods and Applications, MSSU, 5, 1998, 119-132 [in Russian] - - Frobenius type theorems (with A. V. Mikhalev), Proceedings of Workshop on General Algebra and Discrete Mathematics, Germany, Potsdam, 1998, Shaker Verlag Aachen, 1999, 102-112