Generalized matlis duality

Abstract

Let R be a commutative noetherian ring and let E be the minimal injective cogenerator of the category of R-modules. A module M is said to be reflexive with respect to E if the natural evaluation map from M to HomR(HomR(M, E), E) is an isomorphism. We give a classification of modules which are reflexive with respect to E. A module M is reflexive with respect to E if and only if M has a finitely generated submodule S such that M/S is artinian and R/ ann(M) is a complete semi-local ring. ©2000 American Mathematical Society.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1090/s0002-9939-99-05130-8

Keywords

Duality, Matlis

Publication Date

1-1-2000

Journal Title

Proceedings of the American Mathematical Society

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