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Direct products of finite monogenic inverse semigroups

Published online by Cambridge University Press:  14 November 2011

D. C. Trueman
D. C. Trueman
Affiliation:
Monash University, Clayton, Victoria, Australia
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Synopsis

We characterize direct products of finite monogenic inverse semigroups; we show that a finite monogenic inverse semigroup which is not a group is directly indecomposable and that a finite semigroup which is decomposable into a direct product of monogenic inverse semigroups which are not groups is uniquely so decomposable. We determine when a finite semigroup can be decomposed into a direct product of non-group monogenic inverse semigroups and show how the direct factors, if they exist, can be found.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 3-4 , 1982 , pp. 301 - 317
Copyright
Copyright © Royal Society of Edinburgh 1982

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