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Russian Mathematical Surveys, 1969, Volume 24, Issue 1, Pages 15–24
DOI: https://doi.org/10.1070/RM1969v024n01ABEH001335
(Mi rm5447)
 

This article is cited in 6 scientific papers (total in 6 papers)


Series of articles on the multioperator rings and algebras
Subalgebras of free algebras of some varieties of multioperator algebras

S. V. Polin
References:
Abstract: The problem whether subalgebras of free algebras of various varieties are free plays an important role in general algebra. For some varieties of linear algebras over a field the problem was solved by Kurosh [1] and Shirshov [2], [3]. Kurosh [4] introduced the concept of multioperator algebra over a field and proved that every subalgebra of a free multioperator algebra is free. This paper is devoted to a study of varieties of multioperator algebras given by identities of a special form; particular cases are the commutative and anticommutative laws for classical linear algebras. The main result of the paper comprises the freeness theorem mentioned above for subalgebras of a free multioperator algebra, as well as parallel theorems in Shirshov's papers [2] on the freeness of subalgebras of a free commutative and a free anticommutative algebra; the methods of this last article are maintained without essential modifications.
Received: 30.09.1968
Bibliographic databases:
Document Type: Article
UDC: 519.4+519.9
Language: English
Original paper language: Russian
Citation: S. V. Polin, “Subalgebras of free algebras of some varieties of multioperator algebras”, Russian Math. Surveys, 24:1 (1969), 15–24
Citation in format AMSBIB
\Bibitem{Pol69}
\by S.~V.~Polin
\paper Subalgebras of free algebras of some varieties of multioperator algebras
\jour Russian Math. Surveys
\yr 1969
\vol 24
\issue 1
\pages 15--24
\mathnet{http://mi.mathnet.ru//eng/rm5447}
\crossref{https://doi.org/10.1070/RM1969v024n01ABEH001335}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=237404}
\zmath{https://zbmath.org/?q=an:0177.02603|0197.29103}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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