On regularity preservation in a semigroup

Hickey, J.B. (2004) On regularity preservation in a semigroup. Bulletin of the Australian Mathematical Society, 69, pp. 69-86. (doi: 10.1017/S0004972700034274)

Abstract

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: UNSPECIFIED
• Authors: Hickey, J.B.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Bulletin of the Australian Mathematical Society