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On variants of a semigroup

Published online by Cambridge University Press:  17 April 2009

J. B. Hickey
J. B. Hickey
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW.
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Abstract

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If S is a (multiplicative) Semigroup and a ∈ S, the binary operation ∘ defined on the set S by x ∘ y = x a y is associative and the resulting semigroup is called a variant of S. We study the congruence a defined on S by saying that two elements are α-related if and only if they determine the same variant of S. Certain quotients of variants are used to provide an arbitrary semigroup with a generalised local structure. The variant formulation of Nambooripad's partial order on a regular semigroup is used to show that the order possesses a certain property (involving D-equivalence).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 447 - 459
Copyright
Copyright © Australian Mathematical Society 1986

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