This note deals with a finitely generated faithful module E over a commutative semi-prime noetherian ring R, with commutative endomorphism ring HomJ2(Er, E) = Ω(E). It is shown that E is identifiable to an ideal of R whenever Ω(E) lacks nilpotent elements; a class of examples with Ω(E) commutative but not semi-prime is discussed. 1* Main result* Throughout R will denote a commutative noetherian ring and modules will be finitely generated. In order to use the full measure of the ring, we shall consider mostly faithful modules. As for notation, unadorned ® and Horn are taken over the base ring. In case R is semi-prime (meaning here: no nilpotent elements distinct from 0) we recall that its total ring of quotients K is semisimple, and thus a direct sum of fields K — 0Σ Kn 1 ^ i ^ w. Any ideal / of R has the property that Horn (I, /) is commutative and semi-prime: for if S denotes the set of regular elements of R,