子范畴
数学
诺瑟环
等价(形式语言)
纯数学
交换环
局部环
诺瑟人
交换性质
范畴等价
对偶(序理论)
理想(伦理)
域代数上的
戒指(化学)
函子
化学
有机化学
哲学
认识论
作者
Parisa Pourghobadian,Kamran Divaani-Aazar,Ahad Rahimi
出处
期刊:Journal of Commutative Algebra
[Rocky Mountain Mathematics Consortium]
日期:2024-03-01
卷期号:16 (1)
标识
DOI:10.1216/jca.2024.16.95
摘要
We establish the global analogues of some dualities and equivalences in local algebra by developing the theory of relative Cohen–Macaulay modules. Let R be a commutative Noetherian ring (not necessarily local) with identity, and let 𝔞 be a proper ideal of R. The notions of 𝔞-relative dualizing modules and 𝔞-relative big Cohen–Macaulay modules are introduced. With the help of 𝔞-relative dualizing modules, we establish the global analogue of duality on the subcategory of Cohen–Macaulay modules in local algebra. Lastly, we investigate the behavior of the subcategory of 𝔞-relative Cohen–Macaulay modules and 𝔞-relative generalized Cohen–Macaulay modules under Foxby equivalence.
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