The extended centralizer of an S-set

C. V. Hinkle

Vol. 53 (1974), No. 1, 163–170

DOI: 10.2140/pjm.1974.53.163

Abstract

Let S be a semigroup with zero. The extended centralizer Q(M_s) of a right S-set M_s is defined. Necessary and sufficient conditions are given for Q(M_s) to be a regular semigroup. In particular, Q(S_s) is shown to be a regular semigroup when S is regular. We also show that whenever the singular congruence on S is the identity, then Q(S_s) is the injective hull of |S_s and is right self injective.

Mathematical Subject Classification 2000

Primary: 20M10

Milestones

Received: 19 July 1973

Published: 1 July 1974