Almost Lie nilpotent non-prime varieties of associative algebras
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 282-291
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A variety of associative algebras is called
Lie nilpotent if it satisfies the identity $[\cdots[[x_1,x_2],\ldots,x_n]=0$ for some positive integer $n$, where $[x,y] = xy-yx$. We study almost Lie nilpotent varieties, i.e., minimal elements in the set of all varieties that are not Lie nilpotent. We describe all almost Lie nilpotent varieties of algebras over a field of positive characteristic, both finite and infinite, in the cases when the ideals of identities of these varieties are nonprime in the class of all $T$-ideals.
Keywords:
variety of associative algebras, identities of the associated Lie algebra, Lie nilpotency, Engel property.
@article{TIMM_2015_21_4_a26,
author = {O. B. Finogenova},
title = {Almost {Lie} nilpotent non-prime varieties of associative algebras},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {282--291},
publisher = {mathdoc},
volume = {21},
number = {4},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a26/}
}
O. B. Finogenova. Almost Lie nilpotent non-prime varieties of associative algebras. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 282-291. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a26/