Clifford semigroups and seminear-rings of endomorphisms

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
L, then the endomorphisms of S generate a Clifford semigroup E+(S) whose
underlying semilattice is the set of endomorphisms of L These results con-
tribute to the wider theory of seminear-rings of endomorphisms, since E+(S)
has a natural structure as a distributively generated seminear-ring.