论Greenlees-May对偶与Matlis-Greenlees-May等价

关于Matlis自反模

On the Matlis Reflexive Modules

本文系统研究Matlis自反模，证明其构成Krull-Schmidt范畴，并在完备Noetherian局部环上等价于minimax模，建立了完全闭包性质，综述了相关应用与开放问题。

局部素模

Locally prime modules

本文引入局部素模和余素模的概念，通过范畴论技术扩展了Greenlees-May对偶和Matlis-Greenlees-May等价，建立了局部与全局素性之间的联系。

诺特代数上内射包络与平坦覆盖的对偶性

Duality Between Injective Envelopes and Flat Covers over Noether Algebras

本文将交换诺特环上内射包络与平坦覆盖的对偶关系推广到非交换诺特代数领域，拓展了相关同调代数结论的适用范围。

线性紧模的局部同调论

A local homology theory for linearly compact modules

本文引入线性紧模的局部同调论，它在某种意义上与A.格罗滕迪克证明了线性紧模的局部同调模的Noether性、零性和非零性等基本性质。利用Matlis对偶和Macdonald对偶建立了线性紧模的局部同调模与局部上同调模之间的对偶理论。作为对偶定理的结果，我们得到了半离散线性紧模局部上同调理论中一些著名结果的推广。

Flat cotorsion modules over Noether algebras

For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a consequence, we show that pointwise Matlis duality gives a bijective correspondence between the isoclasses of indecomposable injective left modules and the isoclasses of indecomposable flat cotorsion right modules. This correspondence is an explicit realization of Herzog's homeomorphism induced from elementary duality of Ziegler spectra.

Applications of reduced and coreduced modules I

This is the first in a series of papers highlighting the applications of reduced and coreduced modules. Let $R$ be a commutative unital ring and $I$ an ideal of $R$. We show that $I$-reduced $R$-modules and $I$-coreduced $R$-modules provide a setting in which the Matlis-Greenless-May (MGM) Equivalence and the Greenless-May (GM) Duality hold. These two notions have been hitherto only known to exist in the derived category setting. We realise the $I$-torsion and the $I$-adic completion functors as representable functors and under suitable conditions compute natural transformations between them a…