A map f: S ÷ S where S is a semigroup is a retraction if and only if f2 = f, f is a semigroup homomorphism, and f(S) is a two-slded ideal of S. A map f: S ÷ S is a right S-endomorphism if and only if f(xy) = f(x)y for all x,y ~ S. Note that right S-endomorphlsms are also called left translations. It is well-known ([2], [3]) that when S is a semilattice the above two definitions are equivalent. For an arbitrary semlgroup one can easily show that every retraction is a right S-endomorphlsm. In this brief note we utilize a result of Tamura to chamacterize those semlgroups for which the converse is true. Throughout we let S denote a semigroup. Define the equivalence relation -~, on S by x~y if and only if xz E yz for all z C S and set S = {x: x,~a}. Let R be the set of all right Sa endomorphisms on S, and for each a 6 S let k be a