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A NOTE ON LOCAL DUALITY

Published online by Cambridge University Press:  01 January 1997

RICHARD BELSHOFF  and
CAMERON WICKHAM
RICHARD BELSHOFF
Affiliation:
Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, USA
CAMERON WICKHAM
Affiliation:
Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, USA
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Abstract

Let (R, [mfr ]) 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([mfr ], 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.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 1 , January 1997 , pp. 25 - 31
Copyright
© The London Mathematical Society 1997

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