Title

Remarks on reflexive modules, covers, and envelopes

Abstract

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 HomR(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. © 2009 Heldermann Verlag.

Department(s)

Mathematics

Document Type

Article

Keywords

Cover, Envelope, G-dimension, Gorenstein ring, Reflexive module

Publication Date

11-26-2009

Journal Title

Beitrage zur Algebra und Geometrie

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