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Green's relations for regular elements of sandwich semigroups, II; semigroups of continuous functions

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

K. D. Magill Jr  and
S. Subbiah
K. D. Magill Jr
Affiliation:
State University of New York at BuffaloBuffalo, New York 14214USA
S. Subbiah
Affiliation:
Daemen CollegeBuffalo, New York 14226USA
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Abstract

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A sandwich semigroup of continuous functions consists of continuous functions with domains all in some space X and ranges all in some space Y with multiplication defined by fg = foαog where α is a fixed continuous function from a subspace of Y into X. These semigroups include, as special cases, a number of semigroups previously studied by various people. In this paper, we characterize the regular elements of such semigroups and we completely determine Green's relations for the regular elements. We also determine the maximal subgroups and, finally, we apply some of these results to semigroups of Boolean ring homomorphisms.

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1978 , pp. 45 - 65
Copyright
Copyright © Australian Mathematical Society 1978

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