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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generalized Matlis duality


Authors: Richard G. Belshoff, Edgar E. Enochs and Juan Ramon García Rozas
Journal: Proc. Amer. Math. Soc. 128 (2000), 1307-1312
MSC (1991): Primary 13C05; Secondary 13H99
Published electronically: October 18, 1999
MathSciNet review: 1641645
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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 $\Hom _R( \Hom _R(M,E), E)$ 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.


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Additional Information

Richard G. Belshoff
Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
Email: belshoff@math.smsu.edu

Edgar E. Enochs
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: enochs@ms.uky.edu

Juan Ramon García Rozas
Affiliation: Department of Algebra and Analysis, University of Almería 04120 Almería, Spain
Email: jrgrozas@ualm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05130-8
PII: S 0002-9939(99)05130-8
Keywords: Matlis, duality
Received by editor(s): January 28, 1998
Received by editor(s) in revised form: July 1, 1998
Published electronically: October 18, 1999
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society