A note on local duality

Abstract

Let (R, m) be a local Noetherian ring. We show that if R is complete, then an R-module M satisfies local duality if and only if the Bass numbers μi(m, M) are finite for all i. The class of modules with finite Bass numbers includes all finitely generated, all Artinian, and all Matlis reflexive R-modules. If the ring R is not complete, we show by example that modules with finite Bass numbers need not satisfy local duality. We prove that Matlis reflexive modules satisfy local duality in general, where R is any local ring with a dualizing complex.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1112/S0024609396001713

Publication Date

1-1-1997

Journal Title

Bulletin of the London Mathematical Society

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