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Finite semigroups with commuting idempotents

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

C. J. Ash  and
T. E. Hall
C. J. Ash
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
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Abstract

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We show that every such semigroup is a homomorphic image of a subsemigroup of some finite inverse semigroup. This shows that the pseudovariety generated by the finite inverse semigroups consists of exactly the finite semigroups with commuting idempotents.

MSC classification

Secondary: 20M10: General structure theory 20M35: Semigroups in automata theory, linguistics, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 81 - 90
Copyright
Copyright © Australian Mathematical Society 1987

References

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