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Maximal ideals of semigroups of endomorphisms

Published online by Cambridge University Press:  17 April 2009

F.A. Cezus ,
K.D. Magill Jr  and
S. Subbiah
F.A. Cezus
Affiliation:
Department of Mathematics, Valparaiso University, Valparaiso, Indiana, USA;
K.D. Magill Jr
Affiliation:
Department of Mathematics, State University of New York at Buffalo, Amherst, New York, USA;
S. Subbiah
Affiliation:
Department of Mathematics, State University of New York at Buffalo, Amherst, New York, USA.
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Abstract

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The maximal left ideal, the maximal right ideal and the maximal two-sided ideal are all characterized for quite general semigroups of endomorphisms. These results are then applied to such semigroups as the semigroup of all continuous selfmaps of a topological space, the semigroup of all closed selfmaps of a topological space, and the semigroup of all linear endomorphisms of a vector space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 2 , April 1975 , pp. 211 - 225
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Volume I (Math. Surveys 7 (I). Amer. Math. Soc., Providence, Rhode Island, 1961).Google Scholar
[2]Hurewicz, Witold and Wallman, Henry, Dimension theory (Princeton Mathematical Series, 4. Princeton University Press, Princeton, 1941).Google Scholar
[3]Magill, K.D. Jr and Subbiah, S., “Green's relations for regular elements of semigroups of endomorphisms”, Canad. J. Math. (to appear).Google Scholar