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This article is cited in 34 scientific papers (total in 34 papers)
Counterexamples to the Specht problem
A. Ya. Belov
M. V. Lomonosov Moscow State University
Abstract:
The present paper is devoted to the construction of infinitely based varieties of associative algebras over an infinite field of arbitrary positive characteristic.
DOI:
https://doi.org/10.4213/sm460
 Full text:
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English version:
Sbornik: Mathematics, 2000, 191:3, 329–340
Bibliographic databases:
   
UDC:
512.5
MSC: Primary 16R10; Secondary 16R40
Received: 29.10.1998 and 13.10.1999
Citation:
A. Ya. Belov, “Counterexamples to the Specht problem”, Mat. Sb., 191:3 (2000), 13–24; Sb. Math., 191:3 (2000), 329–340
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/msb460https://doi.org/10.4213/sm460 http://mi.mathnet.ru/eng/msb/v191/i3/p13
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 -
Gupta C.K., Krasilnikov A.N., “A simple example of a non-finitely based system of polynomial identities”, Comm. Algebra, 30:10 (2002), 4851–4866
 -
Gupta C.K., “A non-finitely based system of polynomial identities which contains the identity $x^6=0$”, Q. J. Math., 53:2 (2002), 173–183
-
N. I. Sandu, “Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two”, Math. Notes, 74:4 (2003), 569–577
-
Gupta C.K., Krasilnikov A., “The finite basis question for varieties of groups—some recent results”, Illinois J. Math., 47:1-2, Special issue in honor of Reinhold Baer (1902–1979) (2003), 273–283
-
Jackson M., “Semilattices with closure”, Algebra Universalis, 52:1 (2004), 1–37
-
Drensky V., “Polynomial identity rings - Part A - Combinatorial aspects in PI-rings”, Polynomial Identity Rings, Advanced Courses in Mathematics Crm Barcelona, 2004, 1
-
A. N. Vaulin, “On one variety of alternative algebras”, J. Math. Sci., 140:2 (2007), 191–199
-
E. A. Kireeva, A. N. Krasilnikov, “On Some Extremal Varieties of Associative Algebras”, Math. Notes, 78:4 (2005), 503–517
-
Sandu N.I., “Infinite independent systems of the identities of the associative algebra over an infinite field of characteristic $p>0$”, Czechoslovak Math. J., 55:1 (2005), 1–23
-
E. A. Kireeva, “Limit T-spaces”, J. Math. Sci., 152:4 (2008), 540–557
-
A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267
-
Aladova E.V., Krasilnikov A.N., “Polynomial identities in nil-algebras”, Trans. Amer. Math. Soc., 361:11 (2009), 5629–5646
-
Silkin N., “On Finite Basis Property for Joins of Varieties of Associative Rings”, Communications in Algebra, 38:9 (2010), 3187–3205
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Belov-Kanel A., Rowen L., Vishne U., “Structure of Zariski-Closed Algebras”, Transactions of the American Mathematical Society, 362:9 (2010), 4695–4734
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Belov-Kanel A. Rowen L.H. Vishne U., “Full Quivers of Representations of Algebras”, Trans. Am. Math. Soc., 364:10 (2012), 5525–5569
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-
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-
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-
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-
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-
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