On stable equivalences of module subcategories over a semiperfect noetherian ring

Noritsugu Kameyama ; Yuko Kimura ; Kenji Nishida

Colloquium Mathematicae, Tome 135 (2014), p. 7-26 / Harvested from The Polish Digital Mathematics Library

Résumé

Given a semiperfect two-sided noetherian ring Λ, we study two subcategories $_k(Λ) = {M ∈ mod Λ | Ext_{Λ}^{j}(Tr M,Λ) = 0 (1 ≤ j ≤ k)}$ and $_k(Λ) = {N ∈ mod Λ | Ext_{Λ}^{j}(N,Λ) = 0 (1 ≤ j ≤ k)}$ 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.

Détail

Publié le : 2014-01-01

Zbl 1323.16002

EUDML-ID : urn:eudml:doc:284244