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Zaicev, Mikhail Vladimirovich

Statistics Math-Net.Ru
Total publications: 51
Scientific articles: 50
Presentations: 3

Number of views:
This page:4022
Abstract pages:9296
Full texts:3407
References:1105
Professor
Doctor of physico-mathematical sciences (1994)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords: associative algebras, Lie algebras and superalgebras, polynomial identities, growth functions, gradinds.
   
Main publications:
  • Giambruno A, Zaicev M. On codimension growth of finitely generated associative algebras // Advances in Mathematics, 1998, v. 140, p.145–155.
  • Bahturin Yu. A., Mikhalev A. A., Petrogradsky V. M. , Zaicev M. V. Infinite dimensional Lie superalgebras. Walter de Gruyter, Berlin, New York, 1992. x+250 p.
  • Zaitsev M. V. Spetsialnye algebry Li // UMN, 1993, t. 48(6), c. 103–140.
  • Zaitsev M. V., Mischenko S.P. Kriterii polinomialnosti rosta mnogoobrazii superalgebr Li // Izv. RAN. Ser. matem., 1998, t.  62(5), s.  103–116.
  • Giambruno A, Zaicev M. On codimension growth of finitely generated associative algebras // Advances in Mathematics, 1998, v.  140, p.  145–155.
  • Giambruno A, Zaicev M. V. Exponential codimension growth of P. I. algebras: an exact estimate // Advances in Mathematics, 1999, v. 142, p. 221–243.
  • Bahturin Yu. A., Sehgal S. K., Zaicev M. V. Groups gradings on associative algebras // Journal of Algebra, 2001, v. 241, p. 677–698.
  • Zaitsev M. V. Tselochislennost eksponent rosta tozhdestv konechnomernykh algebr Li // Izv. RAN. Ser. matem., 2002, t.  66(3), s.  23–48.
  • Giambruno A., Zaicev M. Minimal varieties of algebras of exponential growth // Advances in Mathematics, 2003, v.  174(2), p.  310–323.
  • Bahturin Yu.  A., Zaicev M. V. Identities of Graded Algebras and Codimension Growth // Trans. Amer. Math. Soc., 2004, v.  356(10), p.  3939–3950.
  • Giambruno A., Zaicev M. Polynomial Identities and Asymptotic Methods, Mathematical Surveys and Monographs, vol. 122, American Mathematical Society, Providence, RI, 2005. xiv+352 p.
  • Giambruno A., Mishchenko S., Zaicev M. Algebras with intermediate growth of the codimensions // Adv. Appl. Math., 2006, v.  37(3), p.  360–377.

http://www.mathnet.ru/eng/person8271
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https://mathscinet.ams.org/mathscinet/MRAuthorID/256798

Publications in Math-Net.Ru
2019
1. M. V. Zaicev, D. D. Repovš, “Combinatorics on binary words and codimensions of identities in left nilpotent algebras”, Algebra Logika, 58:1 (2019),  35–51  mathnet
2. M. V. Zaicev, S. P. Mishchenko, “Codimension sequences and their asymptotic behavior”, Fundam. Prikl. Mat., 22:4 (2019),  115–127  mathnet
2017
3. M. V. Zaicev, “Growth of codimensions of metabelian algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, 6,  15–20  mathnet  mathscinet; Moscow University Mathematics Bulletin, 72:6 (2017), 233–237  isi  scopus
2015
4. M. V. Zaicev, D. Repovš, “Exponential growth of codimensions of identities of algebras with unity”, Mat. Sb., 206:10 (2015),  103–126  mathnet  mathscinet  zmath  elib; Sb. Math., 206:10 (2015), 1440–1462  isi  scopus
5. M. V. Zaicev, “Graded identities in finite-dimensional algebras of codimensions of identities in associative algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, 5,  54–57  mathnet  mathscinet; Moscow University Mathematics Bulletin, 70:5 (2015), 234–236  isi  scopus
2014
6. M. V. Zaicev, D. Repovš, “A Four-Dimensional Simple Algebra with Fractional PI-Exponent”, Mat. Zametki, 95:4 (2014),  538–553  mathnet  mathscinet  elib; Math. Notes, 95:4 (2014), 487–499  isi  scopus
7. A. Giambruno, M. V. Zaicev, “Asymptotic growth of codimensions of identities of associative algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, 3,  54–56  mathnet  mathscinet; Moscow University Mathematics Bulletin, 69:3 (2014), 125–127  scopus
2013
8. O. E. Bezushchak, A. A. Beljaev, M. V. Zaicev, “Codimension growth of algebras with adjoint unit”, Fundam. Prikl. Mat., 18:3 (2013),  11–26  mathnet  mathscinet; J. Math. Sci., 206:5 (2015), 462–473  scopus
2011
9. M. V. Zaitsev, “Identities of unitary finite-dimensional algebras”, Algebra Logika, 50:5 (2011),  563–594  mathnet  mathscinet  zmath; Algebra and Logic, 50:5 (2011), 381–404  isi  scopus
10. O. E. Bezushchak, M. V. Zaitsev, “Exponents of Identities of Group Rings”, Mat. Zametki, 89:5 (2011),  643–651  mathnet  mathscinet; Math. Notes, 89:5 (2011), 605–612  isi  scopus
11. A. B. Verevkin, M. V. Zaicev, S. P. Mishchenko, “A sufficient condition for coincidence of lower and upper exponents of the variety of linear algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, 2,  36–39  mathnet  mathscinet  zmath; Moscow University Mathematics Bulletin, 66:2 (2011), 86–89
2008
12. M. V. Zaitsev, S. P. Mishchenko, “Identities for Lie superalgebras with a nilpotent commutator subalgebra”, Algebra Logika, 47:5 (2008),  617–645  mathnet  mathscinet  zmath  elib; Algebra and Logic, 47:5 (2008), 348–364  isi  elib  scopus
13. Yu. A. Bahturin, M. V. Zaicev, S. K. Sehgal, “Finite-dimensional simple graded algebras”, Mat. Sb., 199:7 (2008),  21–40  mathnet  mathscinet  elib; Sb. Math., 199:7 (2008), 965–983  isi  elib  scopus
14. M. V. Zaicev, S. P. Mishchenko, “An example of a variety of linear algebras with fractional-polynomial growth”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2008, 1,  25–31  mathnet  mathscinet  zmath
2007
15. M. V. Zaicev, S. P. Mishchenko, “Growth of some varieties of Lie superalgebras”, Izv. RAN. Ser. Mat., 71:4 (2007),  3–18  mathnet  mathscinet  zmath  elib; Izv. Math., 71:4 (2007), 657–672  isi  elib  scopus
2006
16. A. Giambruno, S. Mishchenko, M. Zaitsev, “On the growth of the identities of algebras”, Algebra Discrete Math., 2006, 2,  50–61  mathnet  mathscinet  zmath
17. M. V. Zaicev, S. P. Mishchenko, “Colength of varieties of linear algebras”, Mat. Zametki, 79:4 (2006),  553–559  mathnet  mathscinet  zmath  elib; Math. Notes, 79:4 (2006), 511–517  isi  elib  scopus
2003
18. A. Giambruno, M. V. Zaicev, “Minimal varieties of given codimension growth”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2003, 1,  20–22  mathnet  mathscinet  zmath
2002
19. M. V. Zaicev, “Integrality of exponents of codimension growth of finite-dimensional Lie algebras”, Izv. RAN. Ser. Mat., 66:3 (2002),  23–48  mathnet  mathscinet  zmath  elib; Izv. Math., 66:3 (2002), 463–487  scopus
20. A. Giambruno, M. V. Zaicev, “Asymptotics of the codimension growth functions of the standard identity and the Capelli identities”, Uspekhi Mat. Nauk, 57:6(348) (2002),  179–180  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:6 (2002), 1222–1223  isi
21. K. I. Beidar, M. V. Zaicev, S. A. Pikhtilkov, “Lie algebras with maximality condition for Abelian subalgebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, 5,  27–32  mathnet  mathscinet  zmath
2001
22. M. V. Zaicev, S. K. Sehgal, “Finite gradings of simple Artinian rings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2001, 3,  21–24  mathnet  mathscinet  zmath
1999
23. M. V. Zaicev, S. P. Mishchenko, “On the polynomial growth of the colength of varieties of Lie algebras”, Algebra Logika, 38:2 (1999),  161–175  mathnet  mathscinet
24. M. V. Zaicev, S. P. Mishchenko, “Asymptotic behaviour of the colength growth functions of varieties of Lie algebras”, Uspekhi Mat. Nauk, 54:3(327) (1999),  161–162  mathnet  mathscinet  zmath; Russian Math. Surveys, 54:3 (1999), 660–661  isi  scopus
25. Yu. A. Bahturin, M. V. Zaicev, S. K. Sehgal, “$G$-identities of non-associative algebras”, Mat. Sb., 190:11 (1999),  3–14  mathnet  mathscinet  zmath; Sb. Math., 190:11 (1999), 1559–1570  isi  scopus
26. M. V. Zaicev, S. P. Mishchenko, “A new extremal property of the variety $\mathbf{AN}_2$ of Lie algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, 5,  15–18  mathnet  mathscinet  zmath
1998
27. M. V. Zaicev, “A superrank of varieties of Lie algebras”, Algebra Logika, 37:4 (1998),  394–412  mathnet  mathscinet
28. M. V. Zaicev, S. P. Mishchenko, “A criterion for polynomial growth of varieties of Lie superalgebras”, Izv. RAN. Ser. Mat., 62:5 (1998),  103–116  mathnet  mathscinet  zmath; Izv. Math., 62:5 (1998), 953–967  isi  scopus
29. Yu. A. Bahturin, M. V. Zaicev, “Identities of special Jordan algebras with finite grading”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, 2,  26–29  mathnet  mathscinet  zmath
1997
30. M. V. Zaicev, “Varieties of affine Kac–Moody algebras”, Mat. Zametki, 62:1 (1997),  95–102  mathnet  mathscinet  zmath; Math. Notes, 62:1 (1997), 80–86  isi
31. M. V. Zaicev, S. P. Mishchenko, “Varieties of Lie superalgebras of polynomial growth”, Uspekhi Mat. Nauk, 52:2(314) (1997),  165–166  mathnet  mathscinet  zmath; Russian Math. Surveys, 52:2 (1997), 432–433  isi  scopus
32. M. V. Zaicev, “On an extremal variety of Lie superalgebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1997, 6,  18–20  mathnet  mathscinet  zmath
1996
33. M. V. Zaicev, “Identities of affine Kac–Moody algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, 2,  33–36  mathnet  mathscinet  zmath
1995
34. M. V. Zaicev, “Skew-symmetric identities in special Lie algebras”, Mat. Sb., 186:1 (1995),  65–78  mathnet  mathscinet  zmath; Sb. Math., 186:1 (1995), 65–77  isi
35. M. V. Zaicev, “Residual finiteness and representability of Lie algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, 3,  88–91  mathnet  mathscinet  zmath
1994
36. M. V. Zaicev, “Standard identity and Capelli identities in Lie algebras”, Uspekhi Mat. Nauk, 49:2(296) (1994),  153–154  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:2 (1994), 186–187  isi
1993
37. M. V. Zaicev, “Special Lie algebras”, Uspekhi Mat. Nauk, 48:6(294) (1993),  103–140  mathnet  mathscinet  zmath; Russian Math. Surveys, 48:6 (1993), 111–152  isi
38. M. V. Zaicev, “The base rank of varieties of Lie algebras”, Mat. Sb., 184:9 (1993),  21–40  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 80:1 (1995), 15–31  isi
39. M. V. Zaicev, “The standard identity in special varieties of Lie algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1993, 1,  56–59  mathnet  mathscinet  zmath
1992
40. M. V. Zaĭtsev, “On finite separability of relatively free Lie algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, 10,  16–21  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 36:10 (1992), 14–18
41. M. V. Zaicev, “Locally representable varieties of Lie superalgebras”, Mat. Zametki, 52:5 (1992),  33–41  mathnet  mathscinet  zmath; Math. Notes, 52:5 (1992), 1101–1106  isi
42. M. V. Zaicev, “Almost locally representable varieties of Lie algebras”, Mat. Zametki, 51:3 (1992),  9–15  mathnet  mathscinet  zmath; Math. Notes, 51:3 (1992), 225–229  isi
43. M. V. Zaicev, “On the embeddability of relatively free Lie algebras”, Uspekhi Mat. Nauk, 47:4(286) (1992),  191–192  mathnet  mathscinet  zmath; Russian Math. Surveys, 47:4 (1992), 236–237  isi
1991
44. M. V. Zaitsev, S. P. Mishchenko, “Identities of finite-dimensional nilpotent Lie algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, 10,  36–39  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:10 (1991), 32–35
1989
45. M. V. Zaicev, “Locally Hopf varieties of Lie algebras”, Mat. Zametki, 45:6 (1989),  56–60  mathnet  mathscinet  zmath; Math. Notes, 45:6 (1989), 469–472  isi
46. M. V. Zaicev, “Matrix representations of infinite-dimensional Lie algebras”, Uspekhi Mat. Nauk, 44:1(265) (1989),  199–200  mathnet  mathscinet  zmath; Russian Math. Surveys, 44:1 (1989), 267–268  isi
47. M. V. Zaicev, “Locally representable varieties of Lie algebras”, Mat. Sb., 180:6 (1989),  798–808  mathnet  mathscinet  zmath; Math. USSR-Sb., 67:1 (1990), 249–259  isi
1988
48. M. V. Zaicev, “Locally residually finite varieties of Lie algebras”, Mat. Zametki, 44:3 (1988),  352–361  mathnet  mathscinet  zmath; Math. Notes, 44:3 (1988), 674–680  isi
49. M. V. Zaicev, “Residual finiteness and the Noetherian property of finitely generated Lie algebras”, Mat. Sb. (N.S.), 136(178):4(8) (1988),  500–509  mathnet  mathscinet  zmath; Math. USSR-Sb., 64:2 (1989), 495–504
1981
50. M. V. Zaicev, “On decomposability of commutators of varieties of Lie algebras and groups into products”, Mat. Sb. (N.S.), 116(158):3(11) (1981),  315–330  mathnet  mathscinet  zmath; Math. USSR-Sb., 44:3 (1983), 283–297
1980
51. M. V. Zaicev, “Schreier varieties of Lie algebras”, Mat. Zametki, 28:1 (1980),  119–126  mathnet  mathscinet  zmath; Math. Notes, 28:1 (1980), 523–526  isi
1978
52. M. V. Zaicev, “On finitely based varieties of Lie algebras”, Mat. Sb. (N.S.), 106(148):4(8) (1978),  499–506  mathnet  mathscinet  zmath; Math. USSR-Sb., 35:2 (1979), 165–171  isi

2015
53. M. M. Glukhov, M. V. Zaicev, A. S. Kuzmin, V. N. Latyshev, V. T. Markov, A. V. Mikhalev, A. A. Mikhalev, I. A. Chubarov, “Alexandr Alexandrovich Nechaev (7.8.1945–14.11.2014)”, Fundam. Prikl. Mat., 20:1 (2015),  3–7  mathnet  mathscinet; J. Math. Sci., 223:5 (2017), 495–497

Presentations in Math-Net.Ru
1. Коразмерности тождеств конечномерные простых алгебр
M. V. Zaicev
Research Seminar of the Department of Higher Algebra MSU
March 2, 2020
2. Комбинаторика двоичных слов и числовые характеристики тождеств неассоциативных алгебр
M. V. Zaitsev
Research Seminar of the Department of Higher Algebra MSU
December 3, 2018 16:45
3. Комбинаторика 2-ичных слов и функции роста коразмерностей
M. V. Zaitsev
Research Seminar of the Department of Higher Algebra MSU
April 16, 2018 16:45

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