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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

References

Birkoff, G. (1964), Lattice Theory (Amer. Math. Soc., Colloquium Publications 25, Ann Arbor, Mich.).Google Scholar
Dugundji, J. (1966), Topology (Allyn and Bacon, Boston, Mass.).Google Scholar
Gillman, L. and Jerison, M. (1960), Rings of Continuous Functions (D. Van Nostrand, New York).Google Scholar
de Groot, J. (1959), “Groups represented by homeomorphism groups, I”, Math. Annal. 138, 80–102.CrossRefGoogle Scholar
Jacobson, N. (1964), Structure of Rings (Amer. Math. Soc., Colloquium Publications 37, Providence, R.I.).Google Scholar
Kuratowski, K. (1966), Topology, 1 (Academic Press, New York).Google Scholar
Magill, K. D. Jr, (1967), “Semigroup structures for families of functions, II; continuous functions”, J. Austral. Math. Soc. 7, 95–107.Google Scholar
Magill, K. D. Jr, (1970a), “Subgroups of semigroups of functions”, Port. Math. 26, 133–147.Google Scholar
Magill, K. D. Jr, (1970b), “The semigroup of endomorphisms of a Boolean ring”, J. Austral. Math. Soc. 11, 411–416.CrossRefGoogle Scholar
Magill, K. D. Jr, (1974), “Semigroups which admit few embeddings”, Fund. Math. 85, 37–53.CrossRefGoogle Scholar
Magill, K. D. Jr and Subbiah, S. (1974), “Green's relations for regular elements of semigroups of endomorphisms”, Canadian J. Math. 6 (26), 1484–1497.CrossRefGoogle Scholar
Magill, K. D. Jr, and Subbiah, S. (1975), “Green's relations for regular elements of sandwich semigroups, I; general results”, Proc. London Math. Soc. 3 (31), 194–210.CrossRefGoogle Scholar
Sikorski, R. (1969), Boolean Algebras (Springer-Verlag, New York).CrossRefGoogle Scholar