|
This article is cited in 3 scientific papers (total in 3 papers)
On identities of vector spaces embedded in finite associative algebras
I. M. Isaev, A. V. Kislitsin Altai State Pedagogical University
Abstract:
In this paper we study identities of vector spaces embedded in finite associative linear algebras. We prove that a $L$-variety generated by the space of matrices of second order over a finite field has a finite number of $L$-subvarieties. We constructed an example of a finite two-dimensional vector space which has no finite basis of identities. As a corollary, we constructed an example of a finite four-dimensional linear algebra without finite basis of identities. In particular, the authors constructed an example of a ring consisting of 16 elements which has no finite basis of identities.
Keywords:
multiplicative vector space, identity of vector space, $L$-variety, basis of identities, nonfinitely based space, nonfinitely based algebra.
Received: 18.03.2015
Citation:
I. M. Isaev, A. V. Kislitsin, “On identities of vector spaces embedded in finite associative algebras”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:3 (2015), 69–77; J. Math. Sci., 221:6 (2017), 849–856
Linking options:
https://www.mathnet.ru/eng/vngu377 https://www.mathnet.ru/eng/vngu/v15/i3/p69
|
Statistics & downloads: |
Abstract page: | 212 | Full-text PDF : | 61 | References: | 40 | First page: | 4 |
|