Elham Tavasoli, Maryam Salimi: Relative Matlis duality with respect to a semidualizing module, 433-444

Abstract:

Let $R$ be a commutative Noetherian ring and let $C$ be a semidualizing $R$-module. The aim of this paper is to introduce and study the relative version of Matlis duality with respect to $C$ and some other related topics. In particular, it is shown that over local ring $R$, the relative Matlis dual of a Noetherian $R$-module is Artinian, and in the case that $R$ is complete the relative Matlis dual of an Artinian $R$-module is Noetherian.

Key Words: Semidualizing, $C$-injective, Matlis duality.

2020 Mathematics Subject Classification: Primary 13D05; Secondary 13D45, 18G20.

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