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Sibirsk. Mat. Zh., 2017, Volume 58, Number 3, Pages 591–598 (Mi smj2882)  

Simple finite-dimensional algebras without finite basis of identities

A. V. Kislitsinab

a Dostoevsky Omsk State University, Omsk, Russia
b Altaĭ State Pedagogical University, Barnaul, Russia

Abstract: In 1993, Shestakov posed a problem of existence of a central simple finite-dimensional algebra over a field of characteristic 0 whose identities cannot be defined by a finite set (Dniester Notebook, Problem 3.103). In 2012, Isaev and the author constructed an example that gave a positive answer to this problem. In 2015, the author constructed an example of a central simple seven-dimensional commutative algebra without finite basis of identities. In this article we continue the study of Shestakov's problem in the case of anticommutative algebras. We construct an example of a simple seven-dimensional anticommutative algebra over a field of characteristic 0 without finite basis of identities.

Keywords: simple algebra, identity of algebra, basis of identities, nonfinitely based algebra, strongly nonfinitely based algebra.

Funding Agency Grant Number
Russian Science Foundation 16-11-10002
The author was supported by the Russian Science Foundation (Grant 16-11-10002).


DOI: https://doi.org/10.17377/smzh.2017.58.309

Full text: PDF file (273 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:3, 461–466

Bibliographic databases:

UDC: 512.554.1
MSC: 35R30
Received: 04.05.2016

Citation: A. V. Kislitsin, “Simple finite-dimensional algebras without finite basis of identities”, Sibirsk. Mat. Zh., 58:3 (2017), 591–598; Siberian Math. J., 58:3 (2017), 461–466

Citation in format AMSBIB
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