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Subdirectly irreducible Rees matrix semigroups

Published online by Cambridge University Press:  17 April 2009

David E. Zitarelli
David E. Zitarelli
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania, USA.
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Abstract

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Minimal congruences on a Rees matrix semigroup S having at least one proper congruence are described. Necessary and sufficient conditions for S to te subdirectly irreducible are given in two cases according to whether the structure group of S is trivial.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 3 , June 1977 , pp. 351 - 359
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Lallement, Gérard, “Demi-groupes réguliers”, Ann. Mat. Pura Appl. 77 (1967), 47–129.CrossRefGoogle Scholar
[2]Lallement, Gerard, “A note on congruences on Rees matrix semigroups”, Semigroup Forum 8 (1974), 89–92.CrossRefGoogle Scholar
[3]Munn, Walter Douglas, “Embedding semigroups in congruence-free semigroups”, Semigroup Forum 4 (1972), 46–60.CrossRefGoogle Scholar
[4]Petrich, Mario, Introduction to semigroups (Charles E. Merrill, Columbus, Ohio, 1973).Google Scholar
[5]Schein, B.M. [Šaiˇn], “Homomorphisms and subdirect decompositions of semigroups”, Pacific J. Math. 17 (1966), 529–547.CrossRefGoogle Scholar
[6]Trotter, P.O., “Congruence-free inverse semigroups”, Semigroup Forum 9 (1974/1975), 109–116.CrossRefGoogle Scholar