The membership of the local cohomology modules Han (M) of a module M in certain Serre
subcategories of the category of modules is studied from below (i< n) and from above (i> n) …

Let $ R $ be a commutative Noetherian ring with non-zero identity, $\fa $ an ideal of $ R $,
and $ X $ an $ R $--module. In this paper, for fixed integers $ s, t $ and a finite $\fa $--torsion …

Let Φ be a system of ideals of a noetherian ring R and M a finitely generated R-module. We
introduce the notion n-depth (Φ, M) and show that inf {i| dim Supp RH Φ i (M)> n}= n-depth …

Let R be a commutative Noetherian ring, a be an ideal of R and M be a finitely generated R-
module. Melkersson and Schenzel asked whether the set\rm Ass _R\rm Ext^ i_R (R/a^ j, M) …

Serre subcategories and the cofiniteness of generalized local cohomology modules with
respect to a pair of ideals Page 1 International Journal of Algebra and Computation Vol. 26 …

Let R be a commutative Noetherian ring, a an ideal of R and N an R-module. We prove that,
for every finitely generated R-module of finite projective dimension t, the elements in the …

Let $ I $ and $ J $ be two ideals of a commutative Noetherian ring $ R $ and $ M $ be an $ R
$-module. For a non-negative integer $ n $ it is shown that, if the sets $\Ass_R (\Ext^{n} …

Let K be a field and S= K [x 1,…, xn]. Let I be a monomial ideal of S and u 1,…, ur be
monomials in S. We prove that if u 1,…, ur form a filter-regular sequence on S/I, then S/I is …

Let K be a field and I a monomial ideal of the polynomial ring S= K [x1,..., xn] generated by
monomials u1, u2,..., ut. We show that S/I is pretty clean if either: 1) u1, u2,..., ut is a filter …

Abstract Abstract  Let R be a commutative Noetherian ring, $$\frak {a} $$ be an ideal of R
and M be a finitely generated R-module. Melkersson and Schenzel asked whether the set …