Кафедра высшей алгебры

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Tentative list of publications:

The most recent list of publications is available at http://istina.msu.ru/profile/Guterman/

  1. Non-surjective linear transformations of tropical matrices preserving the cyclicity index (with E. Kreines, A. Vlasov) Kybernetika, to appear, 2022
  2. Pairs of maps preserving singularity on subsets of matrix algebras (with A.M. Maksaev, V.V. Promyslov) Linear Algebra and Its Applications, 2022, 644, 1–27
  3. On the lengths of group algebras of finite abelian groups in the semi-simple case (with M.~Khrystik, O.~Markova) Journal of Algebra and its Applications, 2022, 2250140-2250153
  4. On the lengths of group algebras of finite abelian groups in the modular case (with M.A.~Khrystik, O.V. Markova) Journal of Algebra and its Applications, 2022, 2250117-2250130
  5. On the lengths of standard composition algebras (with S.A. Zhilina) Communications in Algebra, 2022, 50:3, 1092-1105
  6. Linear functions preserving Green's relations over fields (with M. Johnson, M. Kambites, A.~Maksaev) Linear Algebra and its Applications, 2021, 611, 310-333
  7. Transformations of assembly number for 4-regular graphs (with E.M. Kreines, N.V. Ostroukhova) Zapiski POMI, 2021, 504 (2021) 21-46.
  8. Linear converters of weak, directional and strong majorizations (with P. Shteyner) Linear Algebra and its Applications, 2021, 613, 320-346
  9. Length function and characteristic sequences of quadratic algebras (with D.K. Kudryavtsev) Journal of Algebra, 2021, 579, 428–455
  10. Integrability of diagonalizable matrices and a dual Schoenberg type inequality (with S. Danielyan, T.W. Ng) Journal of Mathematical Analysis and Applications, 2021, 498:2, 124909, 22 pp
  11. Converting immanants on skew-symmetric matrices (with M.A. Duffner, I.A. Spiridonov) Linear Algebra and its Applications, 2021, 618, 76-96
  12. Symmetrized Birkhoff-James orthogonality in arbitrary normed spaces (with L. Arambašić, B. Kuzma, R. Rajić, S. Zhilina) Journal of Mathematical Analysis and Applications, 2021, 502:1, 125203, 16 pp
  13. Operators preserving mutual strong Birkhoff-James orthogonality on B(H) (with L. Arambašić, B. Kuzma, R. Rajić, S. Zhilin) Linear Algebra and its Applications, 2021, 624, 27-43
  14. Upper bounds on scrambling index for non-primitive digraphs (with A.M. Maksaev) Linear and Multilinear Algebra, 2021, 69:11, 2143-2168
  15. Linear transformations of tropical matrices preserving the cyclicity index (with E. Kreines, C. Thomassen) Special Matrices, 2021, 9, 112-118
  16. Linear immanant converters on skew-symmetric matrices of order 4 (with M.A. Duffner, I.A. Spiridonov) Journal of Mathematical Sciences, 2021, 255:3, 242–253
  17. Relation graphs of the sedenion algebra (with S.A. Zhilina) Journal of Mathematical Sciences, 2021, 255:3, 254–270
  18. Orthograph related to mutual strong Birkhof-James orthogonality in $C^*$-algebras (with L. Arambašić, B. Kuzma, R. Rajić, S. Zhilin) Banach Journal of Mathematical Analysis, 2020, 14:4, 1751 – 1772
  19. The length of the group algebra of the group $Q_8$ (with O.V. Markova) New Trends in Algebras and Combinatorics. World Scientific Publ, 2020, 105-133, doi: 10.1142/9789811215476\_0010
  20. Higher-distance commuting varieties (with M. Elyze, R. Morrison, K. \v{S}ivic) Linear and Multilinear Algebra, 2020, doi: 10.1080/03081087.2020. 1834493
  21. Characteristic sequences of non-associative algebras (with D.K. Kudryavtsev) Communications in Algebra, 48(4), 2020, 1713-1725
  22. Majorization for (0,1)-matrices (with G. Dahl and P. Shteyner) Linear Algebra and Its Applications, 585, 2020, 147-163
  23. Orthogonality for (0,-1) tropical normal matrices (with B. Bakhadly and M. J. de la Puente) Special Matrices, 8, 2020, 40-60
  24. Permanent Polya problem for additive surjective maps (with I.A. Spiridonov) Linear Algebra and Its Applications, 599, 2020, 140-155
  25. Upper bounds for the length of non-associative algebras (with D.K. Kudryavtsev) Journal of Algebra, 544, 2020, 483-497
  26. Linear transformtions preserving majorizations for matrix tuples (with P. Shteyner) Vestnik St.Petersburg University, Mathematics, 53(2), 2020, 136-144
  27. 2-words, their graphs and matrices (with E.M. Kreines and N.V. Ostroukhova) Zapiski Nauch. Sem. POMI, 482, 2019, 45-72
  28. 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
  29. Krauter conjecture on permanents is true (with M.V. Budrevich) Journal of Combinatorial Theory - Series A, 162, 2019, 306-343
  30. Length realizability for pairs of quasi-commuting matrices (with O. Markova, V. Mehrmann) Linear Algebra and Its Applications, 568, 2019, 135-154
  31. More on geometry of Krein space C-numerical range (with R. Lemos and G. Soares) Applied Mathematics and Computation, 352, 2019, 258-269
  32. 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
  33. Additive maps preserving scrambling index are bijective (with A.M. Maksaev) Acta Mathematica Hungarica, 84(1-2), 2018, 19-38
  34. Majorization for matrix classes (with Geir Dahl and Pavel Shteyner) Linear Algebra and Its Applications, 555, 2018, 201-221
  35. Extremal generalized centralizers in matrix algebras (with G. Dolinar, B. Kuzma, O. Markova) Communications in Algebra, 46(7), 2018, 3147-3154
  36. 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
  37. On Hartwig–Nambooripad orders (with X. Mary, P. Shteyner) Semigroup Forum (2018). doi.org/10.1007/s00233-018-9940-7
  38. 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
  39. 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
  40. Maps preserving scrambling index (with Maksaev A.M.) Linear and Multilinear Algebra, 69(4), 2018, 840-851
  41. Converting immanants on singular symmetric matrices (with Duffner A.) Lobachevskii Journal of Mathematics, 38(4), 2017, 630-636
  42. The lengths of the quaternion and octonion algebras (with Kudryavtsev D.K.) Journal of Mathematical Sciences (New York), 224(6), 2017, 826-833
  43. 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
  44. 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
  45. Lengths of quasi-commutative pairs of matrices (with Markova O.V., Mehrmann V.) Linear Algebra and Its Applications, 498, 2016, 450-470
  46. Rank functions of tropical matrices (with Ya. Shitov) Linear Algebra and its Applications, 498, 2016, 326-348
  47. 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.
  48. 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
  49. Continuous monotone matrix maps for orders induced by the group inverse (with Efimov M.A.) Journal of Mathematical Inequalities, 10(1), 2016, 123-133
  50. Lengths of quasi-commutative pairs of matrices (with Markova O.V., Mehrmann V.) Linear Algebra and Its Applications, 498, 2016, 450-470
  51. New matrix partial order based on spectrally orthogonal matrix decomposition (with A. Herrero, N. Thome) Linear and Multilinear Algebra, 64(3), 2016, 362-374
  52. 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
  53. The arctic rank of a Boolean matrix (with Beasley L.B., Shitov Ya. N.) Journal of Algebra, 433, 2015, 168-182
  54. Maps on operators strongly preserving sharp order (with Efimov M.A.) Operators and Matrices, 9(3), 2015, 711-731
  55. Graphs Defined by Orthogonality (with B.R. Bakhadly, O.V. Markova) Journal of Mathematical Sciences (New York), 207(5), 2015, 698-717
  56. Characterizing monotone maps on matrices and operators, Classical and Functional Analysis, Ser. 2-3, Transilvania University Press Brasov, Romania, 2015, 5-16
  57. Immanant conversion on symmetric matrices (with C. Purificacao, A. Duffner) Special Matrices, 2(1), 2014, 1-10.
  58. On the Polya conversion problem for permanents and determinants, Journal of Mathematical Sciences, 187(6), 2014, 782-786
  59. Monotone maps on diagonalizable matrices (with M.A. Efimov), Mathematical Inequalities and Applications, 17(4), 2014, 1441-1452
  60. Tropical Cramer determinants revisited (with M. Akian, S. Gaubert) American Mathematical Society, Contemporary Mathematics, 616, Amer. Math. Soc., Providence, RI, 2014, 1-45
  61. The algebra of semi-magic matrices and its length (with O.V. Markova, S.D. Sochnev) Zapiski POMI, 419, 2013, 52-77.
  62. Commuting graphs and extremal centralizers (with G. Dolinar, B. Kuzma, P. Oblak) Ars Mathematica Contemporanea, 7(2), 2014, 453-459
  63. Commutativity preservers via matrix centralizers (with G. Dolinar, B. Kuzma, P. Oblak) Publicationes Mathematicae Debrecen, 84(3-4) (2014), 439-450
  64. Extremal matrix centralizers (with G. Dolinar, B. Kuzma, P. Oblak) Linear Algebra and its Applications, 438(7), 2013, 2904-2910
  65. Extremal case in Marcus-Oliveira conjecture and beyond (with R. Lemos, and G. Soares) Linear and Multilinear Algebra, 61(9), 2013, 1206-1222
  66. 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
  67. Monotone maps on index one matrices (with M.A. Efimov), Zapiski POMI, 405, 2012, 67-96.
  68. On the Gibson bounds over finite fields (with M.V. Budrevich), Serdica Math. J. 2012, 38, 395-416
  69. 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.
  70. 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.
  71. Permanent has less zeros than determinant over finite fields (with M. Budrevich) American Mathematical Society, Contemporary Mathematics, 579, 2012, 33-42
  72. On the Polya permanent problem over finite fields (with G. Dolinar, B. Kuzma, M. Orel) European Journal of Combinatorics, 32, 2011, 116-132
  73. On Gibson barrier for Polya problem (with G. Dolinar, B. Kuzma), Fundamental and Applied Mathematics, 16(8), 2010, 73-86
  74. Operators preserving primitivity for matrix pairs (with L.B. Beasley), Matrix Methods: Theory, Algorithms, Applications, Word Scientific Publishing, 2010, 2-20
  75. Additive Frobenius endomorphisms for Sylvester and related bounds (with Graca Soares), Contributions to General Algebra, Verlag Johannes Heyn, 19, 2010, 91-102
  76. The correspondence between tropical convexity and mean payoff games (with Marianne Akian, Stephane Gaubert), Mathematical Theory of Networks and Systems, 2010, 1295-1302
  77. 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.
  78. Frobenius endomorphisms of matrix spaces and their applications, Operator Theory and Operator Algebras, 2009, 33-42.
  79. 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.
  80. Frobenius Endomorphisms on matrix spaces (with A.V. Mikhalev), Contemporary Problems of Mathematics and Mechanics, 4(3), 2009, 71-105.
  81. Matrix ranks and linear independence over tropical semirings (with M. Akian, S. Gaubert), American Mathematical Society, Contemporary Mathematics, 495, 2009, 1-33.
  82. Preserving zeros of a polynomial (with B. Kuzma), Communications in Algebra, 37(11), 2009, 3801-3827.
  83. Matrix invariants over semirings, Handbook of Algebra, Elseiver, 6, 2009, 3-33.
  84. The characterization of operators preserving primitivity for matrix k-tuples (with L. B. Beasley), Linear Algebra and its Applications, 430, 2009, 1762-1777.
  85. Commutative matrix subalgebras and length function (with O. V. Markova), Linear Algebra and its Applications, 430, 2009, 1790-1805.
  86. Maps preserving zeros of matrix polynomials (with B. Kuzma), Doklady of Russian Academy of Sciences, Mathematics, 427(3), 2009, 300-302.
  87. Preserving regular tournaments and term rank-1 (with L.B. Beasley, D. Brown), Linear Algebra and its Applications, 431, 2009, 926-936.
  88. Operators preserving primitivity for matrix pairs (with L. B. Beasley), Matrix Methods: Theory, Algorithms, Applications, Word Scientific Publishing, 2008, 2-20.
  89. On linear operators preserving the set of positive polynomials (with B. Shapiro), Journal of Fixed Point Theory and Applications, 3 (2), 2008, 411-429.
  90. Characterization of transformations strongly preserving zeros of matrix polynomials (with B. Kuzma), Uspehi Mat. Nauk, 63(5), 2008, 184-185. [in Russian]
  91. Rank and determinant functions for semirings, London Mathematical Society Lecture Notes, 347, 2007, 1-33.
  92. Transformations preserving matrix invariants over semirings, Idempotent and tropical mathematics and problems of mathematical physics, Moscow, MCCME, 1, 2007, 84-90
  93. Monotone additive transformations on matrices, Mat. Zametki, 81(5), 2007, 681–692.
  94. Monotone matrix mappings defined by the group inverse and simultaneous diagonalizability (with I. I. Bogdanov), Mat. Sbornik, 198(1), 2007, 3-20.
  95. Idempotent matrices and majorisation (with L. B. Beasley, K.-T. Kang, S.-Z. Song), Fundamental and Applied Mathematics, 13(1), 2007, 11-29.
  96. 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
  97. 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
  98. Rank-permutable additive mappings (with A. A. Alieva, B. Kuzma), Linear Algebra Appl., 414, 2006, 607-616
  99. 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
  100. 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
  101. Monotone linear transformations on matrices are invertible (with A. A. Alieva), Communications in Algebra, 33, 2005, 3335-3352
  102. Rank inequalities over semirings (with L. B. Beasley), Journal of Korean Math. Soc., 42(2), 2005, 223-241
  103. Factor rank for nonnegative matrices (with O. A. Vaysman), Chebyshevskii Sbornik, 6(4), 2005, 64-67 [in Russian]
  104. 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]
  105. Linear preservers of rank permutability (with A. A. Alieva), Linear Algebra and its Applications, 384, 2004, 97-108
  106. 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
  107. Linear Transformations Preserving Matrix Invariants (with A.V. Mikhalev), Mathematics. Mechanics. Informatics. 10 years RFFI. Fizmatlit, 2004, 501(3),165-186 [in Russian]
  108. LP-problems for rank inequalities over semirings: factorization rank (with L.B. Beasley), Sovrem. Mat. Prilozh. Algebra, 13, 2004, 53-70 [in Russian]
  109. 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]
  110. 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]
  111. Transformations of non-negative integer matrices preserving the determinant, Uspehi Mat. Nauk, 58(6), 2003 147-148 [in Russian]
  112. Monotone Matrix Maps Preserve Non-Maximal Rank, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, 2003, 311-328
  113. General Algebra and Linear Transformations Preserving Matrix Invariants (with A.V. Mikhalev), Fundamental and Applied Mathematics, 9(1), 2003, 83-101 [in Russian]
  114. Linear transformations that preserve the Dieudonne determinant over an arbitrary division ring, Uspehi Mat. Nauk, 57(4), 2002, 171-172 [in Russian]
  115. Identities of near-triangular matrices, Matem. Sbornik, 192(6), 2001, 3-15
  116. Linear preservers for matrix inequalities and partial orderings, Linear Algebra and its Applications, 331, 2001, 75-87
  117. Frobenius type theorems in the noncommutative case, Linear and Multilinear Algebra, 48(4), 2001, 293-312
  118. Linear preservers for Drazin star partial order, Communications in Algebra, 29(9), 2001, 3905-3917
  119. Linear transformations, preserving super-rank, Mathematical Methods and Applications, MSSU, 8, 2001, 100-104 [in Russian]
  120. Graded local rings, Fundamental and Applied Mathematics, 6(3), 2000, 753-756 [in Russian]
  121. Some general techniques on Linear Preserver Problems (with C.-K. Li, P. Semrl), Linear Algebra and Applications, 315, 2000, 61-81
  122. Singularity preservers over local domains, Journal of Mathematical Sciences, 102(6), 2000, 4591-4597.
  123. On the Growth of Identities (with A.Regev), Algebra. Berlin, New York: Walter de Gruyter, 2000, 319-331
  124. 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
  125. Ph. Hall type theorems for modules (with E. Kreines), Universal Algebra and its Applications, Volgograd, 2000, 60-72
  126. A note on linear preservers of a certain matrix partial order, Formal Power Series and Algebraic Combinatorics, Berlin: Shpringer-Verlag, 2000, 441-446
  127. 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]
  128. P. Hall’s theorem on transversals for modules (with E. Kreines), Fundamental and Applied Mathematics, 5(1), 1999, 119-130 [in Russian]
  129. Identities and codimensions of a certain subalgebra of triangular matrix algebra, Mathematical Methods and Applications, MSSU, 6, 1999, 79-82 [in Russian]
  130. Linear transformations preserving Adjamagbo determinant, Mathematical Methods and Applications, MSSU, 6, 1999, 67-72 [in Russian]
  131. 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]
  132. 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