Vol. 31, No. 2, 1969

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Completely injective semigroups

Edmund H. Feller and Richard Laham Gantos

Vol. 31 (1969), No. 2, 359–366

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
Received: 31 May 1968
Published: 1 November 1969
Edmund H. Feller
Richard Laham Gantos