5 citations · 7 across the 24 of their papers we have counts for
11 papers · 1 filter
Cohomological dimension filtration and annihilators of top local cohomology modules
Ali Atazadeh, Monireh Sedghi, Reza Naghipour
Let denote an ideal in a commutative Noetherian ring and a finitely generated -module. In this paper, we introduce the concept of the cohomological dimension f…
On the annihilators and attached primes of top local cohomology modules
Ali Atazadeh, Monireh Sedghi, Reza Naghipour
Let \frak a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that {\rm Ann}_R(H_{\frak a}^{{\dim M}({\frak a}, M)}(M))= {\rm Ann}_R(M…
On the finiteness of Bass numbers of local cohomology modules and Cominimaxness
Kamal Bahmanpour, Reza Naghipour, Monireh Sedghi
In this paper, we continue the study of cominimaxness modules with respect to an ideal of a commutative Noetherian ring (cf. \cite{ANV}), and Bass numbers of local cohomology modul…
A note on the quintasymptotic prime ideals
Saeed Jahandoust, Reza Naghipour
Let denote a commutative Noetherian ring, an ideal of , and let be a multiplicatively closed subset of . In \cite{Ra1}, Ratliff showed that the sequence of sets $…
Quintasymptotic sequences over an ideal and quintasymptotic cograde
Saeed Jahandoust, Reza Naghipour
Let denote an ideal of a Noetherian ring . The purpose of this article is to introduce the concepts of quintasymptotic sequences over and quintasymptotic cograde of ,…
A new characterization of Cohen-Macaulay rings
Kamal Bahmanpour, Reza Naghipour
The purpose of this article is to provide a new characterization of Cohen-Macaulay local rings. As a consequence we deduce that a local (Noetherian) ring is Gorenstein if and o…
Socle finiteness of local cohomology modules and Gorenstein ideals
Ali Akbar Mehrvarz, Kamal Bahmanpour, Reza Naghipour
The purpose of this paper is to give some equivalent conditions to the socle and Bass numbers' conjectures which raised by C. Huneke in (Problems on local cohomology, Free resoluti…
Cofiniteness of local cohomology modules for ideals of dimension one
Kamal Bahmanpour, Reza Naghipour, Monireh Sedghi
Let denote a commutative Noetherian (not necessarily local) ring, an arbitrary -module and an ideal of of dimension one. It is shown that the -module $\Ext^i_…
On the generalization of Faltings' Annihilator Theorem
Mohammad Reza Doustimehr, Reza Naghipour
Let be a commutative Noetherian ring and let be a non-negative integer. In this article, by using the theory of Gorenstein dimensions, it is shown that whenever is a ho…
Faltings' local-global principle for the minimaxness of local cohomology modules
Mohammad Reza Doustimehr, Reza Naghipour
The concept of Faltings' local-global principle for the minimaxness of local cohomology modules over a commutative Noetherian ring is introduced, and it is shown that this prin…
Faltings' local-global principle for the finiteness of local cohomology modules
Davood Asadollahi, Reza Naghipour
Let (R,m) be a complete local ring, a an ideal of R and M a finitely generated R-module. The aim of this paper is to show that for any non-negative integer n, the least integer i s…