广义局部同调模块的相关素理想的同完备性和有限性

arXiv - MATH - Commutative Algebra Pub Date : 2024-09-08 DOI:arxiv-2409.05090

Alireza Vahidi, Ahmad Khaksari, Mohammad Shirazipour

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引用次数: 0

摘要

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

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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arXiv - MATH - Commutative Algebra

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