Auslander correspondence for kawada rings

Abstract

We study the Auslander ring of a basic left Köthe ring $\Lambda$ and give a characterization of basic left Köthe rings in terms of their Auslander rings. We also study the functor category Mod$((\Lambda$-mod${)}^{\mathrm{op}})$ and characterize basic left Köthe rings $\Lambda$ by using functor categories Mod$((\Lambda$-mod${)}^{\mathrm{op}})$. As a consequence we show that there exists a bijection between the Morita equivalence classes of left Kawada rings and the Morita equivalence classes of Auslander generalized right QF-2 rings.