Articles
Publication Date: 2026
Bulletin des Sciences Mathematiques (00074497)208
We provide a characterization of contravariantly finite resolving subcategories of the module category of finite representation type in terms of their functor rings. Furthermore, we characterize contravariantly finite resolving subcategories of the module category Λ-mod of finite type that contain the Jacobson radical of Λ, by their functor categories. We investigate the pure semisimplicity conjecture for a locally finitely presented category [Figure presented], given that X constitutes a covariantly finite subcategory of Λ-mod and that each simple object within Mod(Xop) is finitely presented; additionally, we offer a characterization of covariantly finite subcategories of finite representation type through the lens of decomposition properties with respect to their closure under filtered colimits. Consequently, we delve into the finiteness and purity of n-cluster tilting subcategories, along with the Gorenstein projective modules of the module categories. © 2025 Elsevier Masson SAS
Publication Date: 2025
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas (15787303)119(1)
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)op) and characterize basic left Köthe rings Λ by using functor categories Mod((Λ-mod)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. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2024.
