Completely injective semigroups

Edmund H. Feller and Richard Laham Gantos

Vol. 31 (1969), No. 2, 359–366

DOI: 10.2140/pjm.1969.31.359

Abstract

A semigroup S with identity is termed completely right injective if every right unitary S-system is injective. The semigroup S is called completely injective if every righl and left unitary S-system is injective. We prove that S is completely injective if and only if S is a semigroup with zero, where every right ideal and every left ideal of S is generated by an idempotent. This condition is equivalent to the statement that S is an inverse semigroup with zero, whose idempotents are dually well-ordered.

Mathematical Subject Classification

Primary: 20.93

Milestones

Received: 31 May 1968

Published: 1 November 1969