Remarks on reflexive modules, covers, and envelopes
The author presents results on reflexive modules over Gorenstein rings which generalize results of Serre and Samuel on reflexive modules over regular local rings. The Gorenstein rings of dimension at most two are characterized 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, the notions of a reflexive cover and a reflexive envelope of a module are introduced and the author shows that every finitely generated \(R\)-module has a reflexive cover, if \(R\) is a Gorenstein local ring of dimension at most two. Finally, it is shown that every finitely generated \(R\)-module has a reflexive envelope, if \(R\) is quasi-normal or if \(R\) is locally an integral domain.
scientific article; zbMATH DE number 5601571