Cofiniteness and finiteness of associated prime ideals of generalized local cohomology modules

Alireza Vahidi, Ahmad Khaksari, Mohammad Shirazipour
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Abstract

Let $n$ be a non-negative integer, $R$ a commutative Noetherian ring, $\mathfrak{a}$ an ideal of $R$, $M$ and $N$ two finitely generated $R$-modules, and $X$ an arbitrary $R$-module. In this paper, we study cofiniteness and finiteness of associated prime ideals of generalized local cohomology modules. In some cases, we show that $\operatorname{H}^{i}_{\mathfrak{a}}(M,X)$ is an $(\operatorname{FD}_{
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广义局部同调模块的相关素理想的同完备性和有限性
假设 $n$ 是一个非负整数,$R$ 是一个交换诺特环,$mathfrak{a}$ 是$R$ 的一个理想,$M$ 和 $N$ 是两个有限生成的$R$ 模块,$X$ 是一个任意的$R$ 模块。在本文中,我们将研究广义局部同调模块的相关素理想的同完备性和完备性。在某些情况下,我们证明 $\operatorname{H}^{i}_{\mathfrak{a}}(M,X)$ 是一个$(\operatorname{FD}_{
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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