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Fundam. Prikl. Mat., 1999, Volume 5, Issue 1, Pages 139–147 (Mi fpm381)  

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

On semilocal semigroup rings

A. V. Zhuchin

Moscow State Institute of Steel and Alloys (Technological University)

Abstract: The approach for study semilocal semigroup rings over non-radical rings based on description the structure of semigroup on the whole is suggested. The following main statement is proved. Let $R$ be a ring, $\overline R=R/J(R)\ne 0$, $S$ be a semigroup with zero $z$. The semigroup ring $RS$ is semilocal if and only if: $(i)$ $R$ is semilocal; $(ii)$ there exists a chain of ideals $ż\}=S_0\subset S_1\subset\ldots\subset S_n=S$ such that $S_i/S_{i-1}$, $1\le i\le n$, are nil or completely $0$-simple; $(iii)$ the contracted semigroup rings $R_0(S_i/S_{i-1})$, are semilocal.

Full text: PDF file (467 kB)

Bibliographic databases:
UDC: 512.552.7
Received: 01.09.1996

Citation: A. V. Zhuchin, “On semilocal semigroup rings”, Fundam. Prikl. Mat., 5:1 (1999), 139–147

Citation in format AMSBIB
\Bibitem{Zhu99}
\by A.~V.~Zhuchin
\paper On semilocal semigroup rings
\jour Fundam. Prikl. Mat.
\yr 1999
\vol 5
\issue 1
\pages 139--147
\mathnet{http://mi.mathnet.ru/fpm381}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1799539}
\zmath{https://zbmath.org/?q=an:0963.16023}


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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. I. B. Kozhukhov, “Radical Semigroup Rings and the Thue–Morse Semigroup”, Math. Notes, 74:4 (2003), 502–509  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. M. F. Nasrutdinov, “Semilocal Group Algebras”, Math. Notes, 78:3 (2005), 375–377  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Mazurek R. Ziembowski M., “on Semilocal, Bezout and Distributive Generalized Power Series Rings”, Int. J. Algebr. Comput., 25:5 (2015), 725–744  crossref  mathscinet  zmath  isi
  • Фундаментальная и прикладная математика
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