Auslander correspondence for kawada rings

TL;DR

This paper characterizes basic left K"othe rings through their Auslander rings and explores the relationship between Kawada rings and Auslander generalized right QF-2 rings using functor categories.

Contribution

It provides a new characterization of basic left K"othe rings via Auslander rings and establishes a bijection between Kawada rings and Auslander generalized right QF-2 rings.

Findings

Characterization of basic left K"othe rings using Auslander rings

Establishment of a bijection between Kawada rings and Auslander generalized right QF-2 rings

Use of functor categories to analyze ring properties

Abstract

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