Let (R, m) be a Noetherian local ring and let ̂R denote the m-adic completion of R. In this
paper, we introduce the concept of the weak goingup property for the extension R⊆ ̂R and …

Assume that ϕ (R, m, k)→(S, n, l) is a local homomorphism between commutative noetherian
local rings R and S. We say that an S-module M is almost finite over R if it is finitely …

Let $ R $ be a commutative noetherian local ring. Denote by $\mod R $ the category of
finitely generated $ R $-modules, and by ${\mathcal G}(R) $ the full subcategory of $\mod R …

ON THE FINITENESS PROPERTIES OF THE GENERALIZED LOCAL COHOMOLOGY
MODULES Page 1 ON THE FINITENESS PROPERTIES OF THE GENERALIZED LOCAL …

Let R be a noetherian ring, 𝔞 an ideal of R such that dim R/𝔞= 1 and M a finite R-module.
We will study cofiniteness and some other properties of the local cohomology modules …

Matlis showed that the injective hull of a simple module over a commutative Noetherian ring
is Artinian. In several recent papers, non-commutative Noetherian rings whose injective …

Let R be a commutative Noetherian ring, α an ideal of R, and M, N two finitely generated R-
modules. We prove that the generalized local cohomology modules Ht α (M, N) are α …

Let R be a commutative Noetherian ring, I an ideal of R, and M an arbitrary R-module. It is
shown that the R-module is finitely generated, for all i≥ 0, if and only if the R-module is …

Let a be an ideal of Noetherian ring R and M a finitely generated R-module such that cd (a,
M)= c. In this paper, we investigate Att R (H ac (M)). Among other things, it is shown that Max …

Let aa be an ideal of a commutative Noetherian ring R and M a finitely generated R-module.
It is shown that\rm Ann _R (H_ a^\rm dim M (M))=\rm Ann _R (M/T_R (a, M)) Ann R (H a dim …