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On stable equivalences of module subcategories over a semiperfect noetherian ring

Noritsugu Kameyama, Yuko Kimura, Kenji Nishida (2014)

Colloquium Mathematicae

Given a semiperfect two-sided noetherian ring Λ, we study two subcategories k ( Λ ) = M m o d Λ | E x t Λ j ( T r M , Λ ) = 0 ( 1 j k ) and k ( Λ ) = N m o d Λ | E x t Λ j ( N , Λ ) = 0 ( 1 j k ) of the category mod Λ of finitely generated right Λ-modules, where Tr M is Auslander’s transpose of M. In particular, we give another convenient description of the categories k ( Λ ) and k ( Λ ) , and we study category equivalences and stable equivalences between them. Several results proved in [J. Algebra 301 (2006), 748-780] are extended to the case when Λ is a two-sided noetherian semiperfect ring.

On the category of modules of second kind for Galois coverings

Piotr Dowbor (1996)

Fundamenta Mathematicae

Let F: R → R/G be a Galois covering and m o d 1 ( R / G ) (resp. m o d 2 ( R / G ) ) be a full subcategory of the module category mod (R/G), consisting of all R/G-modules of first (resp. second) kind with respect to F. The structure of the categories ( m o d ( R / G ) ) / [ m o d 1 ( R / G ) ] and m o d 2 ( R / G ) is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.

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