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Mathematics of the USSR-Sbornik, 1976, Volume 30, Issue 4, Pages 441–447
DOI: https://doi.org/10.1070/SM1976v030n04ABEH002282
(Mi sm2909)
 

This article is cited in 2 scientific papers (total in 2 papers)

Galois extensions of radical algebras

V. K. Kharchenko
References:
Abstract: Suppose $G$ is a finite group of automorphisms of an associative algebra $K$ with an identity element over a field $F$. Let $t(x)=\sum_{g\in G}x^g$. Assume that $\rho$ is a supernilpotent radical which is closed under the taking of subalgebras and satisfies the following condition: if $A\in\rho$ and $M$ is a nonempty set, then the ring $A_M$ of $M\times M$ matrices all but a finite number of whose columns are zero is radical.
THEOREM. If $R$ is a two-sided ideal of $K$ and $K=t(K)K,$ then $t(R)\in\rho$ implies $R\in\rho$.
Examples of radicals satisfying the above conditions are Baer's lower radical, the locally nilpotent radical, the locally finite radical, and also the algebraic kernel and Köthe radical, if $F$ is uncountable.
Bibliography: 5 titles.
Received: 01.03.1976
Bibliographic databases:
UDC: 519.48
Language: English
Original paper language: Russian
Citation: V. K. Kharchenko, “Galois extensions of radical algebras”, Math. USSR-Sb., 30:4 (1976), 441–447
Citation in format AMSBIB
\Bibitem{Kha76}
\by V.~K.~Kharchenko
\paper Galois extensions of radical algebras
\jour Math. USSR-Sb.
\yr 1976
\vol 30
\issue 4
\pages 441--447
\mathnet{http://mi.mathnet.ru//eng/sm2909}
\crossref{https://doi.org/10.1070/SM1976v030n04ABEH002282}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=472891}
\zmath{https://zbmath.org/?q=an:0346.16024}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1976FU24400002}
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  • https://doi.org/10.1070/SM1976v030n04ABEH002282
  • https://www.mathnet.ru/eng/sm/v143/i4/p500
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:357
    Russian version PDF:77
    English version PDF:15
    References:52
    First page:2
     
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