ﻻ يوجد ملخص باللغة العربية
We introduce a notion of generalized local cohomology modules with respect to a pair of ideals $(I,J)$ which is a generalization of the concept of local cohomology modules with respect to $(I,J).$ We show that generalized local cohomology modules $H^i_{I,J}(M,N)$ can be computed by the v{C}ech cohomology modules. We also study the artinianness of generalized local cohomology modules $H^i_{I,J}(M,N).$
Let $mathfrak{a}$ be an ideal of a noetherian (not necessarily local) ring $R$ and $M$ an $R$-module with $mathrm{Supp}_RMsubseteqmathrm{V}(mathfrak{a})$. We show that if $mathrm{dim}_RMleq2$, then $M$ is $mathfrak{a}$-cofinite if and only if $mathrm
Let fa be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-modules. Let cd_{fa}(M,N) denote the supremum of the is such that H^i_{fa}(M,N) eq 0. First, by using the theory of Gorenstein homological dimensions, we obtai
Let $fa$ be an ideal of a local ring $(R,fm)$ and $M$ a finitely generated $R$-module. We investigate the structure of the formal local cohomology modules ${vpl}_nH^i_{fm}(M/fa^n M)$, $igeq 0$. We prove several results concerning finiteness propertie
Let $A$ be a commutative Noetherian ring containing a field $K$ of characteristic zero and let $R= A[X_1, ldots, X_m]$. Consider $R$ as standard graded with $deg A=0$ and $deg X_i=1$ for all $i$. We present a few results about the behavior of the gra
We study the conditions under which the highest nonvanishing local cohomology module of a domain $R$ with support in an ideal $I$ is faithful over $R$, i.e., which guarantee that $H^c_I(R)$ is faithful, where $c$ is the cohomological dimension of $I$