2024/12/27 by Norihiro Hanihara, Hanihara, Norihiro
Mathematics · #Advanced Topics in Algebra #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Holomorphic and Operator Theory #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2412.19625
openalex publication_date 2024/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the category \mathoprefΛ of reflexive modules over a two-sided Noetherian ring Λ. We show that the category \mathoprefΛ is quasi-abelian if and only if Λ satisfies certain Auslander-type condition on the minimal injective resolution of the ring itself. Furthermore, we establish a Morita theorem which characterizes the category of reflexive modules among quasi-abelian categories in terms of generator-cogenerators.