论文标题
关于Serre子类别扩展的辅助性
Cofiniteness with respect to extension of Serre subcategories
论文作者
论文摘要
让$ r $为可交换的noetherian戒指，$ \ frak a $是$ r $，$ \ mathcal {s} $的理想，是$ r $ -modules的任意serre子类别，满足条件$ c _ {\ frak a} $的条件$ c _ {\ frak a} $，让$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {在本文中，我们定义和研究$ \ MATHCAL {NS} $ - $ \ frak a $ - finite模块相对于扩展子类别$ \ mathcal {ns} $，作为经典概念的概括，即$ \ frak a $ - cofinite模块。对于较低的维度，我们表明$ \ frak的经典结果适用于新概念。
Let $R$ be a commutative noetherian ring, $\frak a$ be an ideal of $R$, $\mathcal{S}$ be an arbitrary Serre subcategory of $R$-modules satisfying the condition $C_{\frak a}$ and let $\mathcal{N}$ be the subcategory of finitely generated $R$-modules. In this paper, we define and study $\mathcal{NS}$-$\frak a$-cofinite modules with respect to the extension subcategory $\mathcal{NS}$ as an generalization of the classical notion, namely $\frak a$-cofinite modules. For the lower dimensions, we show that the classical results of $\frak a$-cofiniteness hold for the new notion.
