On the first nonzero Fitting ideal of a module over a UFD (II)

摘要

Let R be a commutative ring with identity and M be a finitely generated R-module. Let I(M) be the first nonzero Fitting ideal of M and T(M) be the torsion submodule of M. Then, I(M) subset of ann(T(M)). Using this result, it is shown that if R is a Noetherian UFD and M is an Artinian module where I(M) = P is a prime ideal of R, then T(M) similar or equal to R/P and also T(M) splits off.