Vol. 53, No. 1, 1974

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The extended centralizer of an S-set

C. V. Hinkle

Vol. 53 (1974), No. 1, 163–170

Let S be a semigroup with zero. The extended centralizer Q(Ms) of a right S-set Ms is defined. Necessary and sufficient conditions are given for Q(Ms) to be a regular semigroup. In particular, Q(Ss) 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(Ss) is the injective hull of |Ss and is right self injective.

Mathematical Subject Classification 2000
Primary: 20M10
Received: 19 July 1973
Published: 1 July 1974
C. V. Hinkle