Cotilting duality for Artinian rings

Abstract

A classical result due to Morita and Azumaya establishes that given two arbitrary rings, any duality between their finitely generated modules is representable by a faithfully balanced bimodule which is a finitely generated injective cogenerator of both rings and, equivalently, these latter are one-sided artinian. We extend this well-known result to the case of a cotilting bimodule, by analysing the duality it represents in the bounded derived categories of the given rings.