Reflexive modules over Gorenstein rings

Abstract

Introduction.The aim of this paper is to show the relevance of a class of commutative noetherian rings to the study of reflexive modules.They include integrally closed domains, group algebras over these, and Gorenstein rings.We will be basically concerned with a ring 7? having the following property: Let M be a finitely generated 7?-module; then M is reflexive If and only if every 7?-sequence of at most two elements is also an Af-sequence.In the rest of this note, using the above characterization, we examine the closeness between free modules and Macaulay modules of maximum dimension in a local Gorenstein ring.Finally, it is proved that over a one-dimensional Gorenstein ring only projective modules have projective endomorphism rings.