Auslander correspondence for kawada rings

2021/05/23 by Ziba Fazelpour, Fazelpour, Ziba, Alireza Nasr‐Isfahani +1
Mathematics · #16D70 #16G60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2105.10898

openalex publication_date 2021/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Left Co-Köthe Rings and Their Characterizations
• On relative Auslander algebras
• A higher dimensional Auslander-Iyama-Solberg correspondence
• Several Characterizations of Left Köthe Rings
• Ascent Properties of Auslander Categories