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
令$ \ mathfrak {a} $是通勤的noetherian环$ r $，$ \ mathcal {s} $ $ r $ -modules的serre子类别满足条件$ c_ \ mathfrak {a a} $ and $ \ \ \ \ \ \ \ \ \ \ \ m natcal {n} $ subcatepatory $ r $ c_ \ mathfrak {a a} $ r $ c_ \ mathfrak $ r $ r $ -modules。在本文中，我们继续研究$ \ MATHCAL {NS} $ - $ \ MATHFRAK {A} $ - 相对于扩展子类别$ \ Mathcal {ns} $的cofinite模块，证明$ \ Mathfrak {a} $ - cofinitessions的某些经典结果$ \ mathcal {ns} $ - $ \ mathfrak {a} $ - cofiniteness $ \ mathrm {dim} r = d $或$ \ mathrm {dim} r/\ mathfrak {a} a} = d-1 $，其中$ d $是一个正面的integer。我们还研究$ \ Mathcal {ns} $ - $ \ MATHFRAK {a} $ - 本地共生模块的辅助性和模块$ \ MATHRM {ext}^i_r（n，m）$和$ \ \ \ \ \ \ \ \ m artrm {tor} _i} _i _i^r（n，m）$。
Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$, $\mathcal{S}$ a Serre subcategory of $R$-modules satisfying the condition $C_\mathfrak{a}$ and $\mathcal{N}$ the subcategory of finitely generated $R$-modules. In this paper, we continue the study of $\mathcal{NS}$-$\mathfrak{a}$-cofinite modules with respect to the extension subcategory $\mathcal{NS}$, show that some classical results of $\mathfrak{a}$-cofiniteness hold for $\mathcal{NS}$-$\mathfrak{a}$-cofiniteness in the cases $\mathrm{dim}R=d$ or $\mathrm{dim}R/\mathfrak{a}=d-1$, where $d$ is a positive integer. We also study $\mathcal{NS}$-$\mathfrak{a}$-cofiniteness of local cohomology modules and the modules $\mathrm{Ext}^i_R(N,M)$ and $\mathrm{Tor}_i^R(N,M)$.
