arXiv subjects

M. Jahangiri

Publications and source records attributed to M. Jahangiri.

6 recordsLinked to original sources

arXiv2026

Bass numbers of local cohomology modules at the first and last non-vanishing levels

Let $R $ be a commutative Noetherian ring, $\mathfrak{a}$ be an ideal of $R$ and $M$ be a finitely generated $R$-module. In this paper, we study the Bass numbers $\{μ^i(\mathfrak{p}, H^j_{\mathfrak{a}}(M))\} $ of local cohomology modules with respect to an ideal $\mathfrak{p}\in Spec(R)$ in each of the following cases: $i\in \{ 0, 1, 2\}$ and $j= grade_{\mathfrak{a}}(M),$ $R$ is regular and $i\in\{ ht(\mathfrak{p}), ht(\mathfrak{p})- 1\}$ and $j= cd_{\mathfrak{a}}(M)$, the cohomological dimension of $M$ with respect to $\mathfrak{a}$.

math.AC↗

arXiv2015

On graded local cohomology modules defined by a pair of ideals

Let $R = \bigoplus_{n \in \mathbb{N}_{0}} R_{n}$ be a standard graded ring, $M$ be a finite graded $R$-module and $J$ be a homogenous ideal of $R$. In this paper we study the graded structure of the $i$-th local cohomology module of $M$ defined by a pair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. More precisely, we discuss finiteness property and vanishing of the graded components $H^{i}_{R_{+},J}(M)_{n}$. Also, we study the Artinian property and tameness of certain submodules and quotient modules of $H^{i}_{R_{+},J}(M)$.

math.AC↗

arXiv2015

On the associated prime ideals of local cohomology modules defined by a pair of ideals

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 $\Ass_R(\Ext^{n} _{R}(R/I,M))$ and $\Supp_R(\Ext^{i}_{R}(R/I,H^{j}_{I,J} (M)))$ are finite for all $i \leq n+1$ and all $j< n$, then so is \linebreak$\Ass_R(\Hom_{R}(R/I,H^{n}_{I,J}(M)))$. We also study the finiteness of $\Ass_R(\Ext^{i}_{R}(R/I,H^{n}_{I,J} (M)))$ for $i=1,2$.

math.AC↗

arXiv2015

On the Attached prime ideals of local cohomology modules defined by a pair of ideals

Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H^{d-1}_{I,J}(M)$ are computed by means of the concept of co-localization. Also, we illustrate the attached prime ideals of $H^{t}_{I,J}(M)$ on a non-local ring $R$, for $t= \dim M$ and $t= cd(I,J,M)$.

math.AC↗

arXiv2011

Tameness and Artinianness of Graded Generalized Local Cohomology Modules

Let $R=\bigoplus_{n\geq 0}R_n$, $\fa\supseteq \bigoplus_{n> 0}R_n$ and $M$ and $N$ be a standard graded ring, an ideal of $R$ and two finitely generated graded $R$-modules, respectively. This paper studies the homogeneous components of graded generalized local cohomology modules. First of all, we show that for all $i\geq 0$, $H^i_{\fa}(M, N)_n$, the $n$-th graded component of the $i$-th generalized local cohomology module of $M$ and $N$ with respect to $\fa$, vanishes for all $n\gg 0$. Furthermore, some sufficient conditions are proposed to satisfy the equality $\sup\{\en(H^i_{\fa}(M, N))| i\geq 0\}= \sup\{\en(H^i_{R_+}(M, N))| i\geq 0\}$. Some sufficient conditions are also proposed for tameness of $H^i_{\fa}(M, N)$ such that $i= f_{\fa}^{R_+}(M, N)$ or $i= \cd_{\fa}(M, N)$, where $f_{\fa}^{R_+}(M, N)$ and $\cd_{\fa}(M, N)$ denote the $R_+$-finiteness dimension and the cohomological dimension of $M$ and $N$ with respect to $\fa$, respectively. We finally consider the Artinian property of some submodules and quotient modules of $H^j_{\fa}(M, N)$, where $j$ is the first or last non-minimax level of $H^i_{\fa}(M, N)$.

math.AC↗

arXiv2008

Asymptotic Behaviour and Artinian Property of Graded Local Cohomology Modules

In this paper, considering the difference between the finiteness dimension and cohomological dimension for a finitely generated module, we investigate the asymptotic behavior of grades of components of graded local cohomology modules with respect to irrelevant ideal; as long as we study some artinian and tameness property of such modules.

math.AC↗