AI 中文总结
本文针对交换诺特环$R$上有限生成$R$-模范畴的特定全子范畴，研究其中挠对的分类问题。
AI 中文摘要
设$R$为交换诺特环，记$\bmod R$为有限生成$R$-模构成的范畴，令$\triangle$为$\text{Spec}\thinspace R$的一个子集，$\text{Ass}^{-1}\triangle$表示$\bmod R$中由相伴素理想属于$\triangle$的有限生成$R$-模组成的全子范畴。本文研究$\text{Ass}^{-1}\triangle$及$\bmod R$的其他若干全子范畴中挠对的分类问题。
英文摘要
Let $R$ be a commutative noetherian ring. Denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules. Let $Δ$ be a subset of $\operatorname{Spec} R$, and let $\operatorname{Ass}^{-1}Δ$ stand for the full subcategory of $\operatorname{mod} R$ consisting of finitely generated $R$-modules whose associated prime ideals belong to $Δ$. In this paper, we consider classifying torsion pairs in $\operatorname{Ass}^{-1}Δ$ and some other full subcategories of $\operatorname{mod} R$.
Comments14 pages
