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Fundam. Prikl. Mat., 1998, Volume 4, Issue 2, Pages 763–767 (Mi fpm314)  

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

Short communications

Finiteness conditions for subdirectly irreducible $S$-acts and modules

I. B. Kozhukhov

Moscow State Institute of Electronic Technology (Technical University)

Abstract: It is proved that, for every semigroup $S$ of $n$ elements, the cardinalities of the subdirectly irreducible $S$-acts are less or equal to $2^{n+1}$. If the cardinalities of the subdirectly irreducible $S$-acts are bounded by a natural number then $S$ is a periodic semigroup. It is obtained a combinatorial proof of the fact that there exist only finitely many of unitary subdirect irreducible modules over a finite ring.

Full text: PDF file (257 kB)

Bibliographic databases:
UDC: 512.531+512.553
Received: 01.02.1997

Citation: I. B. Kozhukhov, “Finiteness conditions for subdirectly irreducible $S$-acts and modules”, Fundam. Prikl. Mat., 4:2 (1998), 763–767

Citation in format AMSBIB
\Bibitem{Koz98}
\by I.~B.~Kozhukhov
\paper Finiteness conditions for subdirectly irreducible $S$-acts and modules
\jour Fundam. Prikl. Mat.
\yr 1998
\vol 4
\issue 2
\pages 763--767
\mathnet{http://mi.mathnet.ru/fpm314}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1801189}
\zmath{https://zbmath.org/?q=an:0968.20035}


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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, A. R. Khaliullina, “Kharakterizatsiya podpryamo nerazlozhimykh poligonov”, PDM, 2015, no. 1(27), 5–16  mathnet
    2. Roueentan M., Sedaghatjoo M., “On Uniform Acts Over Semigroups”, Semigr. Forum, 97:2 (2018), 229–243  crossref  mathscinet  zmath  isi  scopus
    3. I. B. Kozhukhov, A. V. Tsarev, “Abelevy gruppy s finitno approksimiruemymi poligonami”, Fundament. i prikl. matem., 22:5 (2019), 81–89  mathnet
  • Фундаментальная и прикладная математика
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