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Subdirect products of E–inversive semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

H. Mitsch
H. Mitsch
Affiliation:
University of ViennaA-1090 Wien, Austria
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Abstract

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A semigroup S is called E-inversive if for every a ∈ S ther is an x ∈ S such that (ax)2 = ax. A construction of all E-inversive subdirect products of two E-inversive semigroups is given using the concept of subhomomorphism introduced by McAlister and Reilly for inverse semigroups. As an application, E-unitary covers for an E-inversive semigroup are found, in particular for those whose maximum group homomorphic image is a given group. For this purpose, the explicit form of the least group congruence on an arbitrary E-inversive semigroup is given. The special case of full subdirect products of a semilattice and a group (that is, containing all indempotents of the direct product) is investigated and, following an idea of Petrich, a construction of all these semigroups is provided. Finally, all periodic semigroups which are subdirect products of a semilattice or a band with a group are characterized.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 1 , February 1990 , pp. 66 - 78
Copyright
Copyright © Australian Mathematical Society 1990

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