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Mat. Sb. (N.S.), 1973, Volume 92(134), Number 4(12), Pages 530–540 (Mi msb3428)  

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

On the compressive radical of semigroups

E. N. Roiz


Abstract: A centered right $S$-polygon (synonyms: $S$-operand, $S$-system) $A$ is called right compressive if $AS\ne0$ and $\alpha a=\alpha b\to\alpha=0\vee(a,b)\in(\operatorname{Ker}A)_S$ and leftt compressive if $AS\ne0$ and $\alpha a=\beta a\to\alpha=\beta\vee Aa=0$. Here $(\operatorname{Ker}A)_S$ is the congruence on the semigroup $S$ called the kernel of the $S$-polygon $A$ which is defined as follows: $(a,b)\in(\operatorname{Ker}A)_S\leftrightarrow(\forall \alpha\in A)(\alpha a=\alpha b)$.
The intersection of the kernels of all right (left) compressive $S$-polygons is called the right (left) compressive radical of $S$. In this paper we study compressively semisimple and compressively radical semigroups.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 21:4, 523–534

Bibliographic databases:

UDC: 519.47
MSC: Primary 20M10; Secondary 20M30
Received: 23.10.1972

Citation: E. N. Roiz, “On the compressive radical of semigroups”, Mat. Sb. (N.S.), 92(134):4(12) (1973), 530–540; Math. USSR-Sb., 21:4 (1973), 523–534

Citation in format AMSBIB
\Bibitem{Roi73}
\by E.~N.~Roiz
\paper On~the compressive radical of semigroups
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 4(12)
\pages 530--540
\mathnet{http://mi.mathnet.ru/msb3428}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=374304}
\zmath{https://zbmath.org/?q=an:0287.20061}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 4
\pages 523--534
\crossref{https://doi.org/10.1070/SM1973v021n04ABEH002033}


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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. A. G. Sokolsky, “Radicals of semigroups and semigroup algebras”, Sb. Math., 201:5 (2010), 759–783  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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