Induced Modules by an Endomorphism of Finitely Generated Modules

Let R be a commutative ring. A finitely generated R-module M can be converted into an R[X]−module by an R−endomorphism of M (see for example [4]). In this work, we first give a structure Theorem for finitely generated modules over local rings in term of Fitting ideals. And then we consider an R[X]/(f(X))−finitely generated moduleMu,f induced on M by an endomorphism u which annihilate a monic poly-nomial f(X). We establish a structure Theorem for Mu,f which shall have interesting applications in linear algebra