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Certain congruences on a completely regular semigroup

Published online by Cambridge University Press:  18 May 2009

Thomas L. Pirnot
Thomas L. Pirnot
Affiliation:
Kutztown State College, Kutztown, Pennsylvania 19530, U.S.A.
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Congruences on a semigroup S such that the corresponding factor semigroups are of a special type have been considered by several authors. Frequently it has been difficult to obtain worthwhile results unless restrictions have been imposed on the type of semigroup considered. For example, Munn [6] has studied minimum group congruences on an inverse semigroup, R. R. Stoll [9] has considered the maximal group homomorphic image of a Rees matrix semigroup which immediately determines the smallest group congruence on a Rees matrix semigroup. The smallest semilattice congruence on a general or commutative semigroup has been studied by Tamura and Kimura [10], Yamada [12] and Petrich [8]. In this paper we shall study congruences ρ on a completely regular semigroup S such that S/ρ is a semilattice of groups. We shall call such a congruence an SG-congruence.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 2 , September 1974 , pp. 109 - 120
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

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