On stable equivalences of module subcategories over a semiperfect noetherian ring

Noritsugu Kameyama, Yuko Kimura, and Kenji Nishida. "On stable equivalences of module subcategories over a semiperfect noetherian ring." Colloquium Mathematicae 137.1 (2014): 7-26. <http://eudml.org/doc/284244>.

@article{NoritsuguKameyama2014,
abstract = {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.},
author = {Noritsugu Kameyama, Yuko Kimura, Kenji Nishida},
journal = {Colloquium Mathematicae},
keywords = {categories of finitely generated right modules; semiperfect Noetherian rings; -projective modules; syzygies; cosyzygies; approximations; projective covers; stable equivalences; category equivalences},
language = {eng},
number = {1},
pages = {7-26},
title = {On stable equivalences of module subcategories over a semiperfect noetherian ring},
url = {http://eudml.org/doc/284244},
volume = {137},
year = {2014},
}

TY - JOUR
AU - Noritsugu Kameyama
AU - Yuko Kimura
AU - Kenji Nishida
TI - On stable equivalences of module subcategories over a semiperfect noetherian ring
JO - Colloquium Mathematicae
PY - 2014
VL - 137
IS - 1
SP - 7
EP - 26
AB - 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.
LA - eng
KW - categories of finitely generated right modules; semiperfect Noetherian rings; -projective modules; syzygies; cosyzygies; approximations; projective covers; stable equivalences; category equivalences
UR - http://eudml.org/doc/284244
ER -