Completely injective semigroups
Edmund H. Feller, R. L. Gantos · Pacific Journal of Mathematics · 1969
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 right 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.3. E. H. Feller and R. L. Gantos.Completely injectίve semigroups with central idempotents, Glasgrow Math.J. (to appear) 4.