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Semigroups of constant maps

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Boris M. Schein
Affiliation:
Department of Mathematical SciencesUniversity of ArkansasFayetteville, Arkansas 72701, U.S.A.
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Abstract

In this paper “a map” denotes an arbitrary (everywhere defined, or partial, or even multi-valued) mapping. A map is constant if any two elements belonging to its domain have precisely the same images under this map. We characterize those semigroups which can be isomorphic to semigroups of constant maps or to involuted semigroups of constant maps.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Volume 1, (American Mathematical Society, Providence, R.I., 1961).CrossRefGoogle Scholar
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[3]Munn, W. D., ‘Embedding semigroups in congruence-free semigroups’, Semigroup Forum 4 (1972), 4660.CrossRefGoogle Scholar
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Soviet Math. Dokl. 6 (1965), 15631566].Google Scholar
[5]Schein, B. M., ‘Relation algebras and function semigroups’, Semigroup Forum 1 (1970), 162.CrossRefGoogle Scholar
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[7]Tarski, A., ‘Contribution to the theory of models, II’, Nederl. Akad. Wetensch. Proc. Ser. A 57 (1954), 582588.CrossRefGoogle Scholar
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