Simple finite-dimensional algebras without finite basis of identities
- Authors: Kislitsin A.V.1,2
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Affiliations:
- Dostoevsky Omsk State University
- Altaĭ State Pedagogical University
- Issue: Vol 58, No 3 (2017)
- Pages: 461-466
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171212
- DOI: https://doi.org/10.1134/S0037446617030090
- ID: 171212
Cite item
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.
About the authors
A. V. Kislitsin
Dostoevsky Omsk State University; Altaĭ State Pedagogical University
Author for correspondence.
Email: kislitsin@altspu.ru
Russian Federation, Omsk; Barnaul