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Regular semigroups, fundamental semigroups and groups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

D. B. McAlister
D. B. McAlister
Affiliation:
Department of Mathematical Sciences Northern Illinois UniversityDe Kalb, Illinois 60115, U.S.A.
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Abstract

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In this paper we obtain necessary and sufficient conditions on a regular semigroup in order that it should be an idempotent separating homomorphic image of a full subsemigroup of the direct product of a group and a fundamental or combinatorial regular semigroup. The main tool used is the concept of a prehomomrphism θ: S → T between regular semigroups. This is a mapping such that (ab) θ ≦ aθ bθ in the natural partial order on T.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 4 , June 1980 , pp. 475 - 503
Copyright
Copyright © Australian Mathematical Society 1980

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