论文标题
在小维
Cofiniteness with respect to extension of Serre subcategories at small dimensions
论文作者
论文摘要
让$ r $为可交换的noetherian戒指，$ \ frak a $是$ r $，$ \ cs $的理想，是$ r $ - modules的任意serre子类别，让$ \ cn $是有限生成的$ r $ - modules的子类别。在本文中，我们研究了$ \ cn \ cs $ - $ \ frak a $ cofinite模块相对于扩展子类别$ \ cn \ cs $当$ \ dim r/\ frak a \ leq 2 $时。我们还研究了$ \ frak关于新维度的$ cofinitentens。
Let $R$ be a commutative noetherian ring, $\frak a$ be an ideal of $R$, $\cS$ be an arbitrary Serre subcategory of $R$-modules and let $\cN$ be the subcategory of finitely generated $R$-modules. In this paper, we study $\cN\cS$-$\frak a$-cofinite modules with respect to the extension subcategory $\cN\cS$ when $\dim R/\frak a\leq 2$. We also study $\frak a$-cofiniteness with respect to a new dimension.
