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 $\sigma$ 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. 
@article{AL_2013_52_6_a4,
     author = {O. B. Finogenova},
     title = {Almost commutative varieties of associative rings and algebras over a~finite field},
     journal = {Algebra i logika},
     pages = {731--768},
     publisher = {mathdoc},
     volume = {52},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_6_a4/}
}
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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. http://geodesic.mathdoc.fr/item/AL_2013_52_6_a4/