Auslander correspondence for kawada rings

We study the Auslander ring of a basic left K"othe ring $\mathrm{\Lambda }$ and give a characterization of basic left K"othe rings in terms of their Auslander rings. We also study the functor category Mod$((\mathrm{\Lambda }$-mod${)}^{\mathrm{o}\mathrm{p}})$ and characterize basic left K"othe rings $\mathrm{\Lambda }$ by using functor categories Mod$((\mathrm{\Lambda }$-mod${)}^{\mathrm{o}\mathrm{p}})$. 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.