On the Fitting ideals of a multiplication module

Abstract

In this paper, we characterize all finitely generated multiplication \(R\)-modules whose the first nonzero Fitting ideal of them is contained in only finitely many maximal ideals. Also, we prove that a finitely generated multiplication \(R\)-module \(M\) is faithful if and only if \(M\) is a projective of constant rank one \(R\)-module.