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This article is cited in 5 scientific papers (total in 5 papers)
An example of a central simple commutative finite-dimensional algebra with an infinite basis of identities
A. V. Kislitsin Altai State Pedagogical University, ul. Molodezhnaya 55, Barnaul, 656031, Russia
Abstract:
In 1993 I. P. Shestakov came up with the question whether there exists a central simple finite-dimensional algebra over a field of characteristic 0, whose identities are not given by a finite set (Dniester Notebook, Question 3.103). In 2012 I. M. Isaev and the author constructed a desired example, giving an affirmative answer to the question posed. Here research into Shestakov's question is continued for the case of commutative algebras. A seven-dimensional central simple commutative algebra over a field of characteristics 0 having no finite basis of identities is exemplified.
Keywords:
simple algebra, identity of algebra, basis of identities, infinitely based algebra.
Received: 20.11.2014
Citation:
A. V. Kislitsin, “An example of a central simple commutative finite-dimensional algebra with an infinite basis of identities”, Algebra Logika, 54:3 (2015), 315–325; Algebra and Logic, 54:3 (2015), 204–210
Linking options:
https://www.mathnet.ru/eng/al696 https://www.mathnet.ru/eng/al/v54/i3/p315
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Abstract page: | 282 | Full-text PDF : | 49 | References: | 44 | First page: | 17 |
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