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Completely 0-simple semigroups of left quotients

Part of: Semigroups

Published online by Cambridge University Press:  26 February 2010

Mario Petrich
Mario Petrich
Affiliation:
21420 Bol, Brač, Croatia.
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Abstract

A subsemigroup S of a semigroup Q is a left order in Q, and Q is a semigroup of left quotients of S, if every element of Q can be written as a−1b for some a, b∈S with a belonging to a group -class of Q. Necessary and sufficient conditions on a semigroup S are obtained in order that S be a left order in a completely 0-simple semigroup Q. The class of all completely 0-simple semigroups of left quotients of S is related to the set of certain left congruences on S. Axioms are provided for semigroups which occur in the discussion of left orders in completely 0-simple semigroups.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Mathematika , Volume 51 , Issue 1-2 , December 2004 , pp. 111 - 122
Copyright
Copyright © University College London 2004

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