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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 4, Pages 282–291 (Mi timm1250)  

This article is cited in 3 scientific papers (total in 3 papers)

Almost Lie nilpotent non-prime varieties of associative algebras

O. B. Finogenova

Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: 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.

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Bibliographic databases:
UDC: 512.552.4
Received: 01.08.2015

Citation: O. B. Finogenova, “Almost Lie nilpotent non-prime varieties of associative algebras”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 282–291

Citation in format AMSBIB
\Bibitem{Fin15}
\by O.~B.~Finogenova
\paper Almost Lie nilpotent non-prime varieties of associative algebras
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 4
\pages 282--291
\mathnet{http://mi.mathnet.ru/timm1250}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468451}
\elib{http://elibrary.ru/item.asp?id=25301006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. B. Finogenova, “Pochti lievo nilpotentnye mnogoobraziya assotsiativnykh kolets”, Sib. elektron. matem. izv., 12 (2015), 901–909  mathnet  crossref
    2. A. V. Kislitsin, “On nonnilpotent almost commutative $L$-varieties of vector spaces”, Siberian Math. J., 59:3 (2018), 458–462  mathnet  crossref  crossref  isi  elib
    3. A. V. Kislitsin, “The Specht property of $L$-varieties of vector spaces over an arbitrary field”, Algebra and Logic, 57:5 (2018), 360–367  mathnet  crossref  crossref  isi
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