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A Note on Local Duality

A Note on Local Duality 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. 1991 Mathematics Subject Classification 13D45. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

A Note on Local Duality

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References (8)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609396001713
Publisher site
See Article on Publisher Site

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. 1991 Mathematics Subject Classification 13D45.

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Jan 1, 1997

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