MAXIMALITY OF THE FIRST NONZERO FITTING IDEAL OF A MODULE

Let R be a Noetherian 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 constructM, when I(M) is a finite intersection of maximal ideals of R.