محرم آقاپورنهر

Let R be a Noetherian ring, I be an ideal of R and n , d be two non-negative inte- gers.In this thesis, we define a condition Pn(I) for I-cofiniteness of modules and we show if R is of dimension d satisfying Pd−1 (I) for all ideals of dimension d−1, then R it satisfies Pd−1 (I) for all ideals I. Let M be an R-module such that ExtiR ( , MI R is finitely generated for all i ≤ n + 1. We show that if dim = 1, then HI i (MI R is I-cofinite for all i ≤ n and if (R,m) is local with dim = 2, then HI i (M ) is I R I-cofinite for all i < n if and only if HomR ( , HI i (M )) is finitely generated for I all i ≤ n. Finally we prove that if M is an R-module of dimension d such that (0 :H i (M ) I) is finitely generated, then HI i (M ) is Artinian. I) )