Let R be a commutative Noetherian ring, let I be an ideal of R, and let M, N be two finitely
generated R-modules. The aim of this paper is to investigate the I-cofiniteness of …

Let R be a commutative Noetherian ring and I an ideal of R. Let t∈N_0 be an integer, M a
finitely generated R-module and X be an R-module such that \Ext^i_R(R/I,X) is finitely …

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, $\Phi $ a system of ideals of $ R $ and $ M, X $
two $ R $-modules. In this paper, we study the Artinianness and cofiniteness of the module …

Let n and t be non-negative integers, R a commutative Noetherian ring with dim (R)≤ n+ 2,
a an ideal of R, M and N finite R-modules, and X an arbitrary R-module. We prove that if Ext …

Let $\mathfrak {a} $ be an ideal of a commutative noetherian ring $ R $ and $ M, N $ two
finitely generated $ R $-modules. By using a spectral sequence argument, it is shown that if …

Let R be a commutative Noetherian ring with non-zero identity and I be an ideal of R. Let M
and N be two finitely generated R-modules. In this paper it is shown that, if \rmcd(I,R)≦1 and …

Let R be a commutative Noetherian ring with identity, I be an ideal of R and M, N be two R-
modules. Throughout this paper, we denote by idR M and fdR M the injective dimension and …

Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M and X finite
R–modules, and ta non-negative integer such that H ai (M, X) is a–cofinite for all i< t. In this …

In this paper, we study the cofiniteness of generalized local cohomology modules with
respect to an ideal of a commutative Noetherian ring and the class of modules in dimension …