arXiv subjects

M. Y. Sadeghi

Publications and source records attributed to M. Y. Sadeghi.

4 recordsLinked to original sources

arXiv2018

On top local cohomology modules, Matlis duality and tensor products

Let $\mathfrak{a}$ be an ideal of a local ring $(R, \mathfrak{m})$ with $c = \mathrm{cd}(\mathfrak{a},R)$ the cohomological dimension of $\mathfrak{a}$ in $R$. In the case that $c=\dim R$, we first give a bound for depth~$D(H^c_\mathfrak{a}(R))$, where $c>2$ and $(R,\mathfrak{m})$ is complete. Later, $H^c_\mathfrak{a}(R) \otimes_R H^c_\mathfrak{a}(R)$, $D(H^c_\mathfrak{a}(R)) \otimes_R D(H^c_\mathfrak{a}(R))$ and $H^c_\mathfrak{a}(R) \otimes_R D(H^c_\mathfrak{a}(R))$ are examined. In the case $c=\dim R-1$, the set Att$_R H^c_\mathfrak{a}(R)$ is considered.

math.AC↗

arXiv2014

Some results on the local cohomology modules with respect to a pair of ideals

Some affirmative answers are given to Huneke's problems. The calculation of local cohomology modules with respect to an arbitrary pair of ideals $I,J$ can be reduced to calculation of local cohomology modules with respect to a pair of ideala whose first ideal is generated by any $k$-regular sequence in $I$.

math.AC↗

arXiv2012

Upper bounds, cofiniteness, and artinianness of local cohomology modules defined by a pair of ideals

Let $R$ be a commutative noetherian ring, $I,J$ be two ideals of $R$, $M$ be an $R$-module, and $\mathcal{S}$ be a Serre class of $R$-modules. A positive answer to the Huneke$^,$s conjecture is given for a noetherian ring $R$ and minimax $R$-module $M$ of krull dimension less than 3, with respect to $\mathcal{S}$. There are some results on cofiniteness and artinianness of local cohomology modules with respect to a pair of ideals. For a ZD-module $M$ of finite krull dimension and an integer $n\in\mathbb{N}$, if $\lc^{i}_{I,J}(M)\in\mathcal{S}$ for all $i>n$, then $\lc^{i}_{I,J}(M)/\fa^{j}\lc^{i}_{I,J}(M)\in\mathcal{S}$ for any $\fa\in\tilde{W}(I,J)$, all $i\geq n$, and all $j\geq0$. By introducing the concept of Seree cohomological dimension of $M$ with respect to $(I,J)$, for an integer $r\in\mathbb{N}_0$, $\lc^{j}_{I,J}(R)\in\mathcal{S}$ for all $j>r$ iff $\lc^{j}_{I,J}(M)\in\mathcal{S}$ for all $j>r$ and any finite $R$-module $M$.

math.AC↗

arXiv2012

On the local cohomology modules deffined by a pair of ideals and serre subcategories

This paper is concerned about the relation between local cohomology modules defined by a pair of ideals and Serre classes of R-modules, as a generalization of results of J. Azami, R. Naghipour and B. Vakili (2009) and M. Asgharzadeh and M.Tousi (2010). Let R be a commutative Noetherian ring, I, J be two ideals of R and M be an R-module. Let a\in W(I; J) and t \in N_0 be such that Ext^t_R(R/a,M)\in S and Ext^j_R(R/a,H^i_I;J(M))\inS for all i < t and all j>=0. Then for any submodule N of H^t_I;J(M) such that Ext^1_R(R/a;N)\in,we obtain HomR(R=a;H^t_I;J(M)/N)\inS.

math.AC↗