In this paper, we show some results on the non-vanishing of the generalized local
cohomology modules HI i (M, N). In a Cohen–Macaulay local ring (R, m), we prove, by using …

Let $ R $ be a commutative Noetherian ring, $\fa $ an ideal of $ R $, $ M $ an arbitrary $ R $-
module and $ N $ a finite $ R $-module. We prove that\cite [Theorem 2.1]{Mel} and\cite …

Let R be a commutative Noetherian ring, I an ideal of R and M, N finitely generated R-
modules. Let 0 an A Z. This note shows that the least integer i such that dim SuppðH i I ðM …

Let I be an ideal of a Complete Cohen-Macaulay local ring R of dimension n. We wil show
that the natural homomorphism Rto HomR (HcI (KR), HcI (KR)) is an isomorphism provided …

Let (R, m) be a commutative Noetherian local ring, I a proper ideal of R and M a finitely
generated R-module of dimension d. We investigate Falting's finiteness dimension f I (M) …

Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely
generated R-module with finite Krull dimension d, and na non-negative integer. In this …

Let [Formula: see text] be a Noetherian homogeneous ring with local base ring (R0, m0) and
irrelevant ideal R+, let M be a finitely generated graded R-module. In this paper we show …

For a Noetherian ring $ R $ we call an $ R $-module $ M $ cofinite if there exists an ideal $ I
$ of $ R $ such that $ M $ is $ I $-cofinite; we show that every cofinite module $ M $ satisfies …

For a finitely generated module M over a commutative Noetherian ring R, we settle the
Auslander–Reiten conjecture when at least one of Hom R (M, R) and Hom R (M, M) has …

Let R be a commutative Noetherian ring and I, J two ideals of R. Let M be a finitely
generated R-module; it is shown that (1) if dimR/(I+ J)= 0, then Hi I, J (M)/JHi I, J (M) is I …