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This article is cited in 2 scientific papers (total in 2 papers)
Almost commutative varieties of associative rings and algebras over a finite field
O. B. Finogenova El'tsin Ural Federal University, pr. Lenina 51, Yekaterinburg, 620083, Russia
Abstract:
Associative algebras over an associative commutative ring with unity are considered. A variety of algebras is said to be permutative if it satisfies an identity of the form
$$
x_1x_2\cdots x_n=x_{1\sigma}x_{2\sigma}\cdots x_{n\sigma},
$$
where $\sigma$ is a nontrivial permutation on a set $\{1,2,\dots,n\}$. Minimal elements in the lattice of all nonpermutative varieties are called almost permutative varieties. By Zorn's lemma, every nonpermutative variety contains an almost permutative variety as a subvariety. We describe almost permutative varieties of algebras over a finite field and almost commutative varieties of rings. In [Algebra Logika, 51, No. 6, 783–804 (2012)], such varieties were characterized for the case of algebras over an infinite field.
Keywords:
varieties of associative algebras, PI-algebras, permutation identity, almost commutative (permutative) varieties.
Received: 31.07.2013 Revised: 24.09.2013
Citation:
O. B. Finogenova, “Almost commutative varieties of associative rings and algebras over a finite field”, Algebra Logika, 52:6 (2013), 731–768; Algebra and Logic, 52:6 (2014), 484–510
Linking options:
https://www.mathnet.ru/eng/al616 https://www.mathnet.ru/eng/al/v52/i6/p731
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Abstract page: | 226 | Full-text PDF : | 56 | References: | 45 | First page: | 15 |
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