Given two modules M and N over a unit ring R, Hom_R(M, N) denotes the set of all module homomorphisms from M to N. It is an R-module with respect to the addition of maps, (f + g)(x) = f(x) + g(x), and the product defined by (a f)(x) = a f(x) for all a element R.

endomorphism ring | exact functor | module homomorphism