On non-Spechtianness of the variety of associative rings that satisfy the identity $x^{32} = 0$
Author:
A. V. Grishin
Journal:
Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 50-51
MSC (2000):
Primary 16R10
DOI:
https://doi.org/10.1090/S1079-6762-00-00080-9
Published electronically:
July 19, 2000
MathSciNet review:
1777855
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Abstract: In this paper we construct examples of $T$-spaces and $T$-ideals over a field of characteristic 2, which do not have the finite basis property.
- I. V. L′vov, Varieties of associative rings. I, II, Algebra i Logika 12 (1973), 269–297, 363; ibid. 12 (1973), 667–688, 735 (Russian). MR 0389973
- Robert L. Kruse, Identities satisfied by a finite ring, J. Algebra 26 (1973), 298–318. MR 325678, DOI https://doi.org/10.1016/0021-8693%2873%2990025-2
- A. R. Kemer, Finite basability of identities of associative algebras, Algebra i Logika 26 (1987), no. 5, 597–641, 650 (Russian). MR 985840
grish1 A. V. Grishin, On the finite basis property of abstract $T$-spaces, Fundamental’naya i Prikladnaya Matematika 1 (1995), 669–700. (Russian)
grish2 A. V. Grishin, Examples of $T$-spaces and $T$-ideals over a field of characteristic $2$ without the finite basis property, Fundamental’naya i Prikladnaya Matematika 5 (1999), 101–118. (Russian)
lvov I. V. Lvov, Varieties of associative rings. I, Algebra i Logika 12 (1973), 269–297. (Russian)
kruse B. I. Kruse, Identities satisfied by a finite ring, J. Algebra 26 (1973), 298–318.
kemer A. R. Kemer, Finite basability of identities of associative algebras, Algebra i Logika 26 (1987), 597–641; English transl., Algebra and Logic 26 (1987), 362–397.
grish1 A. V. Grishin, On the finite basis property of abstract $T$-spaces, Fundamental’naya i Prikladnaya Matematika 1 (1995), 669–700. (Russian)
grish2 A. V. Grishin, Examples of $T$-spaces and $T$-ideals over a field of characteristic $2$ without the finite basis property, Fundamental’naya i Prikladnaya Matematika 5 (1999), 101–118. (Russian)
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Additional Information
A. V. Grishin
Affiliation:
Department of Mathematics, Moscow State Pedagogical University, Krasnoprudnaya 14, Moscow, Russia
Email:
markov@mech.math.msu.su
Received by editor(s):
March 22, 1999
Published electronically:
July 19, 2000
Communicated by:
Efim Zelmanov
Article copyright:
© Copyright 2000
American Mathematical Society
