On stable equivalences of module subcategories over a semiperfect noetherian ring

• Autorzy: Noritsugu Kameyama , Yuko Kimura , Kenji Nishida
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 13C60: Module categories
• 16E05: Syzygies, resolutions, complexes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 137
• Numer: 1
• Strony: 7-26

Daty

wydano

2014

Twórcy

autor

Noritsugu Kameyama

• Interdisciplinary Graduate School, of Science and Technology, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano, 390-8621, Japan

autor

Yuko Kimura

• Interdisciplinary Graduate School, of Science and Technology, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano, 390-8621, Japan

autor

Kenji Nishida

• Department of Mathematical Sciences, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano, 390-8621, Japan

Identyfikatory

DOI

10.4064/cm137-1-2