Let $\mathfrak {a} $ be an ideal of a commutative Noetherian ring $ R $ and $ M $ a finitely
generated $ R $-module. Let $ t $ be a natural integer. It is shown that there is a finite subset …

Let $ R $ be a Noetherian ring, $\mathfrak a $ be an ideal of $ R $ and $ M $ be a finitely
generated $ R $-module. The aim of this paper is to show that if $ t $ is the least integer such …

A FINITENESS RESULT FOR ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES 1.
Introduction Apparently very little is known about the Page 1 PROCEEDINGS OF THE …

Let $\fa $ denote an ideal of a commutative Noetherian ring $ R $ and $ M $ and $ N $ two
finitely generated $ R $-modules with $\pd M<\infty $. It is shown that if $\fa $ is principal or …

Let 𝔞 be an ideal of a commutative Noetherian ring R with identity and let M and N be two
finitely generated R-modules. Let t be a positive integer. It is shown that is contained in the …

Let be an ideal of Noetherian ring R and let s be a non-negative integer. Let M be an R-
module such that is finite R-module. If s is the first integer such that the local cohomology …

In this note we show that if $ I $ is an ideal of a Noetherian ring $ R $ and $ M $ is a finitely
generated $ R $-module, then for any minimax submodule $ N $ of $ H^{t} _ {I}(M) $ the $ R …

We show that the first non-finitely generated generalized local cohomology modules of a
finite modules M and N over a Noetherian ring R with respect to an ideal of R has only …

Let $ R $ be a commutative Noetherian ring, and let $ I $ and $ J $ be two ideals of $ R $.
Assume that $ R $ is local with the maximal ideal ${\mathfrak {m}} $, we mainly prove that (i) …

Assume R is a local Cohen–Macaulay ring. It is shown that AssR (HlI (R)) is finite for any
ideal I and any integer l provided AssR (H2 (x, y)(R)) is finite for any x, y∈ R and AssR (H3 …