arXiv subjects
Publications and source records attributed to Kh. Ahmadi Amoli.
Let $R$ be a commutative Noetherian ring, $\mathfrak a$ and $\mathfrak b$ ideals of $R$. In this paper, we study the finiteness dimension $f_{\mathfrak a}(M)$ of $M$ relative to $\mathfrak a$ and the $\mathfrak b$-minimum $\mathfrak a$-adjusted depth $λ_{\mathfrak a}^{\mathfrak b}(M)$ of $M$, where the underlying module $M$ is relative Cohen-Macaulay w.r.t $\mathfrak a$. Some applications of such modules are given.
Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite R-module. It is shown that, if (R;m) is a complete local ring, then under certain conditions a contains a regular element on DR(Hc a(M)), where c = cd(a;M). A non-zerodivisor characterization of relative Cohen-Macaulay modules w.r.t a is given. We introduce the concept of relative Cohen-Macaulay filtered modules w.r.t a and study some basic properties of such modules. In paticular, we provide a non-zerodivisor characterization of relative Cohen-Macaulay filtered modules w.r.t a. Furthermore, a characterization of cohomological dimension filtration of M by the associated prime ideals of its factors is established. As a consequence, we present a cohomological dimension filtration for those modules whose zero submodule has a primary decomposition. Finally, we bring some new results about relative Cohen- Macaulay modules w.r.t a.
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 $H^{i}_{R_{+},J}(M)$.
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 $i=1,2$.
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 $t= cd(I,J,M)$.