Geodesic
Almost commutative varieties of associative rings and algebras over a~finite field
Algebra i logika, Tome 52 (2013) no. 6, pp. 731-768.

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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 σ is a nontrivial permutation on a set {1,2,…,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.
Mots-clés : varieties of associative algebras, PI-algebras, permutation identity, almost commutative (permutative) varieties. 
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O. B. Finogenova. Almost commutative varieties of associative rings and algebras over a~finite field. Algebra i logika, Tome 52 (2013) no. 6, pp. 731-768. https://geodesic-test.mathdoc.fr/item/AL_2013_52_6_a4/

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