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Rees matrix semigroups with 4-dimensional sandwich matrices

Rees matrix semigroups with 4-dimensional sandwich matrices Acta Mathematiea Academiae Scientiarum Hungarlcae Tomus 35 (3--4), (1980), 339--350. REES MATRIX SEMIGROUPS WITH 4-DIMENSIONAL SANDWICH MATRICES By I. SZABO (Budapest) 1. Introduction Rees' well-known theorem characterizes the completely 0-simple semigroups by means of regular Rees matrix semigroups over groups with zero. In his paper [7], O. STHNFELD introduces the notion of similarly decomposable semigroups which are generalizations of completely 0-simple semigroups and he proves that similarly decomposable semigroups are isomorphic to locally regular Rees matrix semigroups over semigroups with zero and identity elements. In their papers, G. LALLEMENT and M. PETmCH [5] and E. HOTZEL [3] investigate some further semigroup classes which can be characterized by means of Rees matrix semigroups over semigroups with zero and identity elements. In these characterizations the product of the Rees matrices is defined by a sandwich matrix. Our purpose is to give some semigroup classes which can be characterized by means of Rees matrix semigroups over semi- groups with zero and with no identity element. In his paper [2], H.-J. HOF.HNKB further generalizes O. Steinfeld's result. He gives a general class of semigroups (that of the homogeneously decomposable semi- groups) and proves that they are also isomorphic some Rees matrix semigroups. But http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Academiae Scientiarum Hungarica Springer Journals

Rees matrix semigroups with 4-dimensional sandwich matrices

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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general
ISSN
0001-5954
eISSN
1588-2632
DOI
10.1007/BF01886304
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Abstract

Acta Mathematiea Academiae Scientiarum Hungarlcae Tomus 35 (3--4), (1980), 339--350. REES MATRIX SEMIGROUPS WITH 4-DIMENSIONAL SANDWICH MATRICES By I. SZABO (Budapest) 1. Introduction Rees' well-known theorem characterizes the completely 0-simple semigroups by means of regular Rees matrix semigroups over groups with zero. In his paper [7], O. STHNFELD introduces the notion of similarly decomposable semigroups which are generalizations of completely 0-simple semigroups and he proves that similarly decomposable semigroups are isomorphic to locally regular Rees matrix semigroups over semigroups with zero and identity elements. In their papers, G. LALLEMENT and M. PETmCH [5] and E. HOTZEL [3] investigate some further semigroup classes which can be characterized by means of Rees matrix semigroups over semigroups with zero and identity elements. In these characterizations the product of the Rees matrices is defined by a sandwich matrix. Our purpose is to give some semigroup classes which can be characterized by means of Rees matrix semigroups over semi- groups with zero and with no identity element. In his paper [2], H.-J. HOF.HNKB further generalizes O. Steinfeld's result. He gives a general class of semigroups (that of the homogeneously decomposable semi- groups) and proves that they are also isomorphic some Rees matrix semigroups. But

Journal

Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals

Published: Jun 15, 2005

References

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    Lajos, S.; Szép, J.
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    Lallement, G.; Petrich, M.
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    Márki, L.
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    Steinfeld, O.
  • On a class of lattice-ordered semigroups
    Szabó, I.