Reflexive modules and Auslander-type conditions

Abstract

We study the category $\mathop{\mathrm{ref}}\Lambda$ of reflexive modules over a two-sided Noetherian ring $\Lambda$. We show that the category $\mathop{\mathrm{ref}}\Lambda$ is quasi-abelian if and only if $\Lambda$ 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.