Throughout R is a commutative Noetherian ring with nonzero identity, a is an ideal of R, and
n is a nonnegative integer. We write Spec (R)≥ n={p∈ Spec (R): dim (R/p)≥ n}, AssR (X)≥ …

Let $(R,{\mathfrak {m}}) $ be a commutative Noetherian local ring, and let $ I $ and $ J $ be
two proper ideals of $ R $. Let $ M $ be a non-zero finitely generated $ R-$ module. We …

Let (R, 𝔪) be a complete Noetherian local ring and let M be a finite R-module of positive
Krull dimension n. It is shown that any subset T of Assh R (M) can be expressed as the set of …

On the Attached Prime Ideals of Local Cohomology Modules Page 1 Communications in
Algebra®, 41: 3648–3651, 2013 Copyright © Taylor & Francis Group, LLC ISSN: 0092-7872 …

Let $ R $ be a regular local ring containing a field $ k $ of characteristic $ p $ and $ M $ be
an $\mathscr {F} $-finite module. In this paper, we study the injective dimension of $ M $. We …

Let M be a non-zero finitely generated module over a commutative Noetherian local ring (R,
𝔪). In this paper we consider when the local cohomology modules are finitely generated. It is …

Assume that $ R $ is a commutative Noetherian ring with non-zero identity, $\mathfrak {a} $
is an ideal of $ R $, $ X $ is an $ R $--module, and $ t $ is a non-negative integer. In this …

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 R be a commutative Noetherian ring and M, N be two finitely generated R-modules. In
this note, we prove the cofiniteness of generalized local cohomology modules H^ i _ I (M, N) …

Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module.
We explore the behavior of the two notions fa (M), the finiteness dimension of M with respect …