A note on the first nonzero Fitting ideal of a module

Let R be a commutative ring and M be a finitely generated R-module. Let I(M) be the first nonzero Fitting ideal of M. In this paper we characterize some modules over Noetherian UFDs, whose first nonzero Fitting ideal is a prime ideal. We show that if P is a prime ideal and M is a finitely generated R-module with I(M) = P and T(M_P)\neq ۰, then M is isomorphic to R/P \oplus N, for some projective R-module N of constant rank. Also, we investigate some conditions under which {M}/T(M) is free.

کلیدواژه ها:

Fitting ideals ، torsion submodule