J Austral Math Soc Ser A 49 pp59--71, 1990.

Weakly Reductive Semigroups with Atomistic Congruence Lattices

Karl Auinger

(Received 30 January 1989; revised 17 May 1989)

Abstract

The structure of semigroups with atomistic congruence lattices (that is, each congruence is the supremum of the atoms it contains) is studied. For the weakly reductive case the problem of describing the structure of such semigroups is solved up to simple and congruence free semigroups, respectively. As applications, all commutative, finite, completely semisimple semigroups, respectively, with atomistic congruence lattices are described.

1980 AMS Subject Classification (1985 Revision): 20M10, 08A30

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Authors

Karl Auinger: Institut für Mathematik, Universität Wien, A-1090 Wien, Austria.

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Last Modified: Wed Feb 19 10:27:52 2003