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Sibirsk. Mat. Zh., 2010, Volume 51, Number 4, Pages 890–903 (Mi smj2133)  

This article is cited in 1 scientific paper (total in 1 paper)

The unitary closure property of the prime varieties of associative algebras

L. M. Samoĭlov

Ulyanovsk State University, Ulyanovsk, Russia

Abstract: We prove that every prime variety of associative algebras over an infinite field of characteristic $p>$0 is generated by either a unital algebra or a nilalgebra of bounded index. We show that the Engel verbally prime T-ideals remain verbally prime as we impose the identity $x^{p^N}=0$ for sufficiently large $N$. We then describe all prime varieties in an interesting class of varieties of associative algebras.

Keywords: polynomial identity, prime variety, Engel identity.

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English version:
Siberian Mathematical Journal, 2010, 51:4, 712–722

Bibliographic databases:

UDC: 512.552.4
Received: 16.09.2009

Citation: L. M. Samoǐlov, “The unitary closure property of the prime varieties of associative algebras”, Sibirsk. Mat. Zh., 51:4 (2010), 890–903; Siberian Math. J., 51:4 (2010), 712–722

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    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
  • Сибирский математический журнал Siberian Mathematical Journal
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