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Weakly reductive semigroups with atomistic congruence lattices

Part of: Algebraic structures Semigroups

Published online by Cambridge University Press:  09 April 2009

Karl Auinger
Karl Auinger
Affiliation:
Institut für MathematikUniversität WienA-1090 Wien, Austria
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Abstract

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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.

MSC classification

Secondary: 20M10: General structure theory 08A30: Subalgebras, congruence relations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 1 , August 1990 , pp. 59 - 71
Copyright
Copyright © Australian Mathematical Society 1990

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