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Clifford semigroups and monotonicity

Published online by Cambridge University Press:  17 April 2009

T.E. Hays
T.E. Hays
Affiliation:
Department of Mathematics, Ohio State University, Newark, Ohio 43055, USA.
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Abstract

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A semigroup S is said to be monotone if its binary operation is a monotone function from S × S into S. This paper utilizes some of the known algebraic structure of Clifford semigroups, semigroups which are unions of groups, to study topological Clifford semigroups which are monotone. It is shown that such semigroups are preserved under products, homomorphisms, and, under certain conditions, closures. Necessary and sufficient conditions for monotonicity of groups, paragroups, bands, compact orthodox Clifford semigroups, and compact bands of groups are developed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 1 , August 1985 , pp. 83 - 92
Copyright
Copyright © Australian Mathematical Society 1985

References

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