CLIFFORD SEMIGROUPS AND SEMINEAR-RINGS OF ENDOMORPHISMS

Abstract

We consider the structure of the semigroup of self-mappings of a semigroup S under pointwise composition, generated by the endomorphisms of S. We show that if S is a Clifford semigroup, with underlying semilattice Λ, then the endomorphisms of S generate a Clifford semigroup E+(S) whose underlying semilattice is the set of endomorphisms of Λ. These results contribute to the wider theory of seminear-rings of endomorphisms, since E+(S) has a natural structure as a distributively generated seminear-ring.