Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 50, No. 2, pp. 353-362 (2009)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 2, pp. 353-362 (2009) |
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Remarks on reflexive modules, covers, and envelopesRichard BelshoffDepartment of Mathematics, Missouri State University, Springfield, Missouri 65897, e-mail: RBelshoff@MissouriState.eduAbstract: We present results on reflexive modules over Gorenstein rings which generalize results of Serre and Samuel on reflexive modules over regular local rings. We characterize Gorenstein rings of dimension at most two by the property that the dual module $\Hom_R(M, R)$ has G-dimension zero for every finitely generated $R$-module $M$. In the second section we introduce the notions of a reflexive cover and a reflexive envelope of a module. We show that every finitely generated $R$-module has a reflexive cover if $R$ is a Gorenstein local ring of dimension at most two. Finally we show that every finitely generated $R$-module has a reflexive envelope if $R$ is quasi-normal or if $R$ is locally an integral domain. Keywords: reflexive module, cover, envelope, G-dimension, Gorenstein ring Classification (MSC2000): 13C13, 13H10; 13D05, 13C10 Full text of the article (for subscribers):
Electronic version published on: 28 Aug 2009. This page was last modified: 11 Sep 2009.
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