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Guterman, Alexander Èmilevich
Doctor of physico-mathematical sciences (2008)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 22.07.1975
E-mail: ,
Keywords: linear transformations, matrices, rings, matrix invariants.
UDC: 512.54, 512.552, 512.552.12, 512.553, 512.64, 512.643, 512.717, 519.112
MSC: 15A04, 15A33

Subject:

Linear Algebra and its Applications, Transformations Preserving Matrix Invariants, Algebraic Combinatorics, Max-algebras and their Applications, Noncommutative Rings, PI-Algebras.
   
Main publications:
  • A. E. Guterman, Monotone additive transformations on matrices, Mathematical Notes, 81(5), 2007, 681–692.
  • I. I. Bogdanov, A. E. Guterman, Monotone matrix transformations defined by the group inverse and simultaneous diagonalizability, Matematicheskii Sbornik, 198(1), 2007, 3–20.
  • L. B. Beasley, A. E. Guterman, K.-T. Kang, S.-Z. Song, Idempotent Boolean matrices and majorization, Fundamental and Applied Mathematics, 13(1), 2007, 11–29.
  • L. B. Beasley, A. E. Guterman, S.-G. Lee, S.-Z. Song, Frobenius and Dieudonne theorems over semirings, Linear and Multilinear Algebra, 55(1), 2007, 19–34.
  • L. B. Beasley, A. E. Guterman, Y.-B. Jun, S.-Z. Song, Linear preservers of extremes of rank inequalities over semirings: the row and column ranks, Linear Algebra Appl., 413, 2006, 495–509.
  • A. A. Alieva, A. E. Guterman, B. Kuzma, Rank-permutable additive mappings, Linear Algebra Appl., 414, 2006, 607–616.
  • L. B. Beasley, A. E. Guterman, C. L. Neal, Linear preservers for Sylvester and Frobenius bounds on matrix rank, Rocky Mountain Journal of Mathematics, 86(1), 2006, 67–80.
  • L. B. Beasley, A. E. Guterman, S.-G. Lee, S.-Z. Song, Linear preservers of zeros of matrix polynomials, Linear Algebra and its Applications, 401, 2005, 325–340.
  • A. A. Alieva, A. E. Guterman, Monotone linear transformations on matrices are invertible, Communications in Algebra, 33, 2005, 3335–3352.
  • L. B. Beasley, A. E. Guterman, Linear Preservers of Extremes of Rank Inequalities over Semirings: The Factor Rank, J. of Math. Sciences, 131(5), 2005, 5919–5938.
  • A. A. Alieva, A. E. Guterman, Linear preservers of rank permutability, Linear Algebra and its Applications, 384, 2004, 97–108.
  • L. B. Beasley, A. E. Guterman, S.-G. Lee, S.-Z. Song, Linear transformations preserving the Grassmannian over $M_n({\bf Z}+)$, Linear Algebra and its Applications, 393, 2004, 39–46.
  • A. A. Alieva, A. E. Guterman, Rank permutability and additive operators preserving some rank product conditions, Fundamental and Applied Mathematics, 10(4), 2004, 3–14.
  • L. B. Beasley, A. E. Guterman, S.-C. Yi , Linear preservers of extremes of rank inequalities over semirings: term rank and zero-term rank, Fundamental and Applied Mathematics, 10(2), 2004, 3–21.
  • A. E. Guterman, A.V. Mikhalev, General algebra and linear transformations preserving matrix invariants, Fundamental and Applied Mathematics, 9(1), 2003, 83–101.
  • A. E. Guterman, Transformations of non-negative integer matrices preserving the determinant, Uspehi Mat. Nauk, 58(6), 2003, 147–148.
  • A. A. Alieva, A. E. Guterman, Linear transformations preserving rank-commutativity, Bull. of the Moscow State University. Ser. 1. Mathematics. Mechanics, 2003, no. 6, 11–17.
  • A. E. Guterman, Monotone Matrix Maps Preserve Non-Maximal Rank, Combinatorial Methods in Polynomial Identities, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, 2003, 311–328.
  • A. E. Guterman, Linear transformations that preserve the Dieudonne determinant over an arbitrary division ring, Uspehi Mat. Nauk, 57(4), 2002, 171–172.
  • A. Guterman, Linear preservers for matrix inequalities and partial orderings, Linear Algebra and Applications, 331, 2001, 75–87.
  • A. E. Guterman, Frobenius type theorems in the noncommutative case, Linear and Multilinear Algebra, 48(4), 2001, 293–312.
  • A. E. Guterman, Identities of near-triangular matrices, Matem. Sbornik, 192(6), 2001, 3–15.
  • A. Guterman, Linear preservers for Drazin partial order, Communications in Algebra, 29(9), 2001, 3905–3917.
  • A. Guterman, C.-K. Li, P. Semrl, Some general techniques on Linear Preserver Problems, Linear Algebra and Applications, 315, 2000, 61–81.
  • A. Guterman, Singularity preservers over local domains, Journal of Mathematical Sciences, 102(6), 2000, 4591–4597.
  • A. Regev, A. Guterman, On the Growth of Identities, Algebra. Berlin, New York: Walter de Gruyter, 2000, 319–331.

https://www.mathnet.ru/eng/person8758
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/663252
https://elibrary.ru/author_items.asp?authorid=101837
ISTINA https://istina.msu.ru/workers/421534

Publications in Math-Net.Ru Citations
2024
1. A. V. Vlasov, A. E. Guterman, E. M. Kreines, “On linear transformations preserving cyclicity index of nonnegative matrices”, Fundam. Prikl. Mat., 25:1 (2024),  67–82  mathnet
2. A. E. Guterman, E. R. Shafeev, “Frobenius and Sylvester inequalities for the chainable rank”, Zap. Nauchn. Sem. POMI, 534 (2024),  35–56  mathnet
3. A. E. Guterman, S. A. Zhilina, K. D. Mukhanov, “Geometry of varieties of mutually orthogonal matrices”, Zap. Nauchn. Sem. POMI, 534 (2024),  5–34  mathnet
2023
4. A. V. Vlasov, A. E. Guterman, E. M. Kreines, “Linear transformations preserving minimal values of the cyclicity index of tropical matrices”, Zap. Nauchn. Sem. POMI, 524 (2023),  18–35  mathnet 1
2022
5. B. Bakhadly, A. Guterman, M. J. de la Puente, “Normal tropical $(0,-1)$-matrices and their orthogonal sets”, Fundam. Prikl. Mat., 24:1 (2022),  5–30  mathnet; J. Math. Sci., 269:5 (2023), 614–631
6. A. E. Guterman, I. M. Evseev, A. A. Taranenko, “Values of the permanent function on multidimensional $(0,1)$-matrices”, Sibirsk. Mat. Zh., 63:2 (2022),  316–333  mathnet; Siberian Math. J., 63:2 (2022), 262–276 1
7. Yu. A. Alpin, A. E. Guterman, E. R. Shafeev, “An upper bound for the chainable index”, Zap. Nauchn. Sem. POMI, 514 (2022),  5–17  mathnet
2021
8. A. E. Guterman, E. M. Kreines, N. V. Ostroukhova, “Transformations of assembly number for 4-regular graphs”, Zap. Nauchn. Sem. POMI, 504 (2021),  21–46  mathnet
2020
9. A. E. Guterman, S. A. Zhilina, “Cayley–Dickson split-algebras: Doubly alternative zero divisors and relation graphs”, Fundam. Prikl. Mat., 23:3 (2020),  95–129  mathnet; J. Math. Sci., 269:3 (2023), 331–355 5
10. A. E. Guterman, P. M. Shteyner, “Linear operators preserving majorization of matrix tuples”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:2 (2020),  217–229  mathnet; Vestn. St. Petersbg. Univ., Math., 7:2 (2020), 136–144 4
11. A. E. Guterman, S. A. Zhilina, “Relation graphs of the sedenion algebra”, Zap. Nauchn. Sem. POMI, 496 (2020),  61–86  mathnet 2
12. A. E. Guterman, M. A. Duffner, I. A. Spiridonov, “Linear immanant converters on skew-symmetric matrices of order $4$”, Zap. Nauchn. Sem. POMI, 496 (2020),  43–60  mathnet
2019
13. A. E. Guterman, D. K. Kudryavtsev, O. V. Markova, “Length of a direct sum of nonassociative algebras”, Zap. Nauchn. Sem. POMI, 482 (2019),  73–86  mathnet
14. A. E. Guterman, E. M. Kreines, N. V. Ostroukhova, “2-words: their graphs and matrices”, Zap. Nauchn. Sem. POMI, 482 (2019),  45–72  mathnet 1
15. A. E. Guterman, S. V. Danielyan, “On the integral of a polynomial with multiple roots”, Zap. Nauchn. Sem. POMI, 482 (2019),  28–44  mathnet
2018
16. A. E. Guterman, O. V. Markova, “The length of group algebras of small-order groups”, Zap. Nauchn. Sem. POMI, 472 (2018),  76–87  mathnet 5
17. A. E. Guterman, S. A. Zhilina, “Relation graphs of real Cayley–Dickson algebras”, Zap. Nauchn. Sem. POMI, 472 (2018),  44–75  mathnet 6
18. M. V. Budrevich, A. E. Guterman, M. A. Duffner, “Permanent preserving linear transformations of skew-symmetric matrices”, Zap. Nauchn. Sem. POMI, 472 (2018),  31–43  mathnet 4
2017
19. A. Guterman, G. Soares, “On the determinantal range of matrix products”, Zap. Nauchn. Sem. POMI, 463 (2017),  94–111  mathnet; J. Math. Sci. (N. Y.), 232:6 (2018), 805–815  scopus 1
20. A. E. Guterman, O. V. Markova, “Orthogonality graphs of matrices over skew fields”, Zap. Nauchn. Sem. POMI, 463 (2017),  81–93  mathnet; J. Math. Sci. (N. Y.), 232:6 (2018), 797–804  scopus 8
21. A. Guterman, X. Mary, P. Shteyner, “Partial orders based on inverses along elements”, Zap. Nauchn. Sem. POMI, 463 (2017),  58–80  mathnet; J. Math. Sci. (N. Y.), 232:6 (2018), 783–796  scopus 1
22. M. V. Budrevich, A. E. Guterman, K. A. Taranin, “On the Kräuter–Seifter theorem on permanent divisibility”, Zap. Nauchn. Sem. POMI, 463 (2017),  25–35  mathnet; J. Math. Sci. (N. Y.), 232:6 (2018), 760–767  scopus 2
2016
23. A. E. Guterman, E. M. Kreines, Qing-Wen Wang, “Monotone linear transformations on matrices over semirings”, Fundam. Prikl. Mat., 21:1 (2016),  105–122  mathnet; J. Math. Sci., 233:5 (2018), 675–686  scopus
24. A. E. Guterman, D. K. Kudryavtsev, “The lengths of the quaternion and octotion algebras”, Zap. Nauchn. Sem. POMI, 453 (2016),  22–32  mathnet  mathscinet; J. Math. Sci. (N. Y.), 224:6 (2017), 826–832  scopus 8
2015
25. A. E. Guterman, O. V. Markova, “The realizability problem for values of the length function for quasi-commuting matrix pairs”, Zap. Nauchn. Sem. POMI, 439 (2015),  59–73  mathnet  mathscinet; J. Math. Sci. (N. Y.), 216:6 (2016), 761–769  scopus 2
26. M. V. Budrevich, A. E. Guterman, K. A. Taranin, “On divisibility for the permanents of $(\pm1)$-matrices”, Zap. Nauchn. Sem. POMI, 439 (2015),  26–37  mathnet  mathscinet; J. Math. Sci. (N. Y.), 216:6 (2016), 738–745  scopus 3
2014
27. B. R. Bakhadly, A. E. Guterman, O. V. Markova, “Graphs defined by orthogonality”, Zap. Nauchn. Sem. POMI, 428 (2014),  49–80  mathnet; J. Math. Sci. (N. Y.), 207:5 (2015), 698–717  scopus 14
2013
28. A. E. Guterman, O. V. Markova, S. D. Sochnev, “Algebra of semimagic matrices and its length”, Zap. Nauchn. Sem. POMI, 419 (2013),  52–76  mathnet; J. Math. Sci. (N. Y.), 199:4 (2014), 400–413  scopus 3
2012
29. A. È. Guterman, G. Dolinar, B. Kuzma, “Pólya Convertibility Problem for Symmetric Matrices”, Mat. Zametki, 92:5 (2012),  684–698  mathnet  mathscinet  zmath  elib; Math. Notes, 92:5 (2012), 624–635  isi  elib  scopus 4
30. A. E. Guterman, M. A. Efimov, “Monotone maps on matrices of index one”, Zap. Nauchn. Sem. POMI, 405 (2012),  67–96  mathnet  mathscinet; J. Math. Sci. (N. Y.), 191:1 (2013), 36–51  scopus 12
2010
31. G. Dolinar, A. E. Guterman, B. Kuzma, “On the Gibson barrier for the Pólya problem”, Fundam. Prikl. Mat., 16:8 (2010),  73–86  mathnet  mathscinet; J. Math. Sci., 185:2 (2012), 224–232  scopus 5
2009
32. A. È. Guterman, V. K. Lyubimov, A. M. Raigorodskii, S. A. Usachev, “On the Independence Number of Distance Graphs with Vertices in $\{-1,0,1\}^n$”, Mat. Zametki, 86:5 (2009),  794–796  mathnet  mathscinet  zmath  elib; Math. Notes, 86:5 (2009), 744–746  isi  scopus 6
2008
33. A. È. Guterman, B. Kuzma, “On transformations strongly preserving the zeros of matrix polynomials”, Uspekhi Mat. Nauk, 63:5(383) (2008),  185–186  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:5 (2008), 965–967  isi  elib  scopus 1
2007
34. L. B. Beasley, A. È. Guterman, K. Kang, S. Song, “Idempotent Boolean matrices and majorization”, Fundam. Prikl. Mat., 13:1 (2007),  11–29  mathnet  mathscinet  zmath; J. Math. Sci., 152:4 (2008), 456–468  scopus 5
35. A. È. Guterman, “Monotone Additive Matrix Transformations”, Mat. Zametki, 81:5 (2007),  681–692  mathnet  mathscinet  zmath  elib; Math. Notes, 81:5 (2007), 609–619  isi  scopus 12
36. I. I. Bogdanov, A. È. Guterman, “Monotone matrix transformations defined by the group inverse and simultaneous diagonalizability”, Mat. Sb., 198:1 (2007),  3–20  mathnet  mathscinet  zmath  elib; Sb. Math., 198:1 (2007), 1–16  isi  elib  scopus 9
2004
37. A. A. Alieva, A. È. Guterman, “Rank permutability and additive operators preserving related rank product conditions”, Fundam. Prikl. Mat., 10:4 (2004),  3–14  mathnet  mathscinet  zmath; J. Math. Sci., 140:2 (2007), 177–185  scopus 1
38. L. B. Beasley, A. È. Guterman, S. Yi, “Linear preservers of extremes of rank inequalities over semirings: term-rank and zero-term-rank”, Fundam. Prikl. Mat., 10:2 (2004),  3–21  mathnet  mathscinet  zmath; J. Math. Sci., 137:6 (2006), 5179–5191  scopus 3
2003
39. A. È. Guterman, A. V. Mikhalev, “General algebra and linear transformations preserving matrix invariants”, Fundam. Prikl. Mat., 9:1 (2003),  83–101  mathnet  mathscinet  zmath; J. Math. Sci., 128:6 (2005), 3384–3395  scopus 7
40. A. È. Guterman, “Transformations of non-negative integer-valued matrices that preserve the determinant”, Uspekhi Mat. Nauk, 58:6(354) (2003),  147–148  mathnet  mathscinet  zmath; Russian Math. Surveys, 58:6 (2003), 1200–1201  isi  scopus 3
41. A. A. Alieva, A. È. Guterman, “Linear mappings preserving rank commutativity”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2003, no. 6,  11–17  mathnet  mathscinet  zmath
2002
42. A. È. Guterman, “Linear maps preserving the Dieudonné determinant over an arbitrary skew field”, Uspekhi Mat. Nauk, 57:4(346) (2002),  171–172  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:4 (2002), 807–808  isi  scopus
2001
43. A. È. Guterman, “Identities of nearly triangular matrices”, Mat. Sb., 192:6 (2001),  3–14  mathnet  mathscinet  zmath  elib; Sb. Math., 192:6 (2001), 795–806  isi  scopus
2000
44. A. È. Guterman, “Graded local rings”, Fundam. Prikl. Mat., 6:3 (2000),  753–756  mathnet  mathscinet  zmath
1999
45. A. È. Guterman, E. M. Kreines, “Ph. Hall's theorem on transversals for modules”, Fundam. Prikl. Mat., 5:1 (1999),  119–130  mathnet  mathscinet  zmath
2022
46. V. A. Artamonov, L. A. Bokut', V. V. Borisenko, E. I. Bunina, V. M. Buchstaber, A. È. Guterman, Yu. L. Ershov, M. V. Zaitsev, A. Ya. Kanel'-Belov, A. R. Kemer, A. V. Mikhalev, S. P. Mishchenko, S. P. Novikov, A. Yu. Ol'shanskii, Yu. G. Prokhorov, Yu. P. Razmyslov, A. I. Shafarevich, I. V. Shestakov, “Victor Nikolaevich Latyshev (obituary)”, Uspekhi Mat. Nauk, 77:1(463) (2022),  177–182  mathnet  mathscinet  zmath; Russian Math. Surveys, 77:1 (2022), 165–170  isi
2021
47. K. K. Andreev, G. N. Arzhantseva, V. A. Artamonov, V. S. Atabekyan, I. N. Balaba, N. V. Bezverkhny, A. A. Vdovina, V. S. Guba, A. E. Guterman, G. S. Deryabina, N. M. Dobrovolsky, M. V. Zaicev, A. L. Kanunnikov, A. A. Klyachko, O. V. Kulikova, O. V. Markova, V. H. Mikaelyan, M. V. Milentyeva, A. E. Minasyan, K. V. Mikhailovsky, A. V. Mikhalev, A. E. Pankratiev, Yu. G. Prokhorov, Yu. S. Semenov, D. A. Timashev, V. N. Chubarikov, I. A. Chubarov, E. E. Shirshova, “Alexander Yuryevich Olshanskii (to the 75th anniversary)”, Chebyshevskii Sb., 22:2 (2021),  347–365  mathnet
2020
48. N. M. Adrianov, V. A. Artamonov, I. N. Balaba, Yu. A. Bahturin, L. A. Bokut', V. V. Borisenko, E. I. Bunina, S. A. Gaifullin, S. T. Glavatsky, I. Z. Golubchik, S. González, A. V. Grishin, A. È. Guterman, N. I. Dubrovin, M. V. Zaicev, E. I. Zel'manov, N. K. Il'ina, A. Ya. Kanel-Belov, A. L. Kanunnikov, E. S. Kislitsyn, A. A. Klyachko, I. B. Kozhukhov, E. M. Kreines, O. V. Kulikova, T. P. Lukashenko, O. V. Markova, C. Martínez, A. A. Mikhalev, A. V. Mikhalev, A. Yu. Ol'shanskii, A. E. Pentus, A. V.A. Petrov, Yu. G. Prokhorov, S. V. Pchelintsev, V. V. Tenzina, D. A. Timashev, A. A. Tuganbaev, I. N. Tumaikin, V. K. Kharchenko, I. A. Chubarov, A. A. Shafarevich, A. I. Shafarevich, I. P. Shestakov, E. E. Shirshova, V. É. Shpil'rain, “Viktor Timofeevich Markov (21.06.1948—15.07.2019)”, Fundam. Prikl. Mat., 23:2 (2020),  3–16  mathnet; J. Math. Sci., 262:5 (2022), 592–602

Presentations in Math-Net.Ru
1. Values of permanent and positive solution of Wang-Krauter problem
A. È. Guterman
Beijing–Moscow Mathematics Colloquium
April 23, 2021 11:00
2. On the values of permanent function
A. È. Guterman
Iskovskikh Seminar
September 10, 2020 18:00
3. Matrix Centralizers and their Applications
A. È. Guterman

April 14, 2020 16:20   
4. Функция перманента матриц и ее значения
A. È. Guterman

April 9, 2020 19:10
5. Linear transformations preserving matrix invariants
A. È. Guterman
International workshop "Syntax and semantics of logical systems"
August 13, 2019 10:30
6. Функция перманента: алгебраические решения комбинаторных задач
A. È. Guterman
MIPT Interdepartmental Seminar on Discrete Mathematics
April 11, 2018 18:30
7. Проблема Полиа для перманента
A. È. Guterman

May 25, 2017 09:20   
8. Tropical linear algebra and its applications
A. È. Guterman
Algebraic topology and its applications. Postnikov memorial seminar
February 26, 2013 16:45

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