On some properties of -supplemented modules.
Given a semiperfect two-sided noetherian ring Λ, we study two subcategories and 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 and , 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.
Let F: R → R/G be a Galois covering and (resp. ) 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 and is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.