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On regularity preservation in 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, Scotland, e-mail: jbh@maths.gla.ac.uk
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We consider certain subsets of a semigroup S, defined mainly by conditions involving regularity preservation. In particular, the regular base B(S) of S may be regarded as a generalisation of the zero ideal in a semigroup with zero; if it non-empty then S is E-inversive. The other subsets considered are related in a natural way either to B(S) or to the set RP(S) of regularity-preserving elements in S. In a regular semigroup (equipped with the Hartwig-Nambooripad order) each of these subsets contains either minimal elements only or maximal elements only. The relationships between the subsets are discussed, and some characterisations of completely simple semigroups are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 69 - 86
Copyright
Copyright © Australian Mathematical Society 2004

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