Reflexive modules and Auslander-type conditions

Abstract

We study the category $\mathrm{ref}\hat{I}›$ of reflexive modules over a two-sided Noetherian ring $\hat{I}›$. We show that the category $\mathrm{ref}\hat{I}›$ is quasi-abelian if and only if $\hat{I}›$ satisfies certain Auslander-type condition on the minimal injective resolution of the ring itself. Furthermore, we establish a Morita theorem which characterizes the category of reflexive modules among quasi-abelian categories in terms of generator-cogenerators.

19 pages