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Pseudo-idempotents in semigroups of functions

Published online by Cambridge University Press:  09 April 2009

Frank A. Cezus
Frank A. Cezus
Affiliation:
The Australian National University, Canberra, A. C. T.
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The aim of this paper is to generalize Theorem 2.10 (i) of [2]. As stated in [2] this theorem deals with the semigroup of all selfmaps on a discrete space and provides a characterization of H-classes which contain an idempotent. We will generalize this theorem to the case of other semigroups of functions on a discrete space, some semigroups of continuous functions on non-discrete topological spaces, and one semigroup of binary relations. The results in this paper form the main part of chapter 3 of [1]. Some results will be quoted from [1] without proof; the required proofs can easily be supplied by the reader.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 2 , September 1974 , pp. 182 - 187
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Cezus, F., Green's Relations in Semigroups of Functions (Ph.D. thesis submitted 05, 1972 at the Australian National University).Google Scholar
[2]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups (Math. Surveys, No. 7, Amer. Math. Soc., 1961 and 1967).Google Scholar
[3]Magill, K. D. Jr, ‘Subsemigroups of S(X)’, Math. Japonicae 11 (1966), 109–115.Google Scholar
[4]Magill, K. D. Jr, ‘Semigroup structures for families of functions. I’, J. Austral. Math. Soc. 7 (1967), 81–94.CrossRefGoogle Scholar