On the First Nonzero Fitting Ideal of a Module Over a UFD

摘要

Let R be a Noetherian unique factorization domain (UFD) and M be a finitely generated R-module. Let I(M) be the first nonzero Fitting ideal of M. The main result of this paper (Theorem 2.2) characterizes all modules M over a local ring (R, P) with I(M) = P and asserts that for such modules, pd(M) = 1 or pd(M) = gldim(R). We also construct M when I(M) is a finite intersection of maximal ideals of R.