PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On stable equivalences of module subcategories over a semiperfect noetherian ring

Volume 137 / 2014

Noritsugu Kameyama, Yuko Kimura, Kenji Nishida Colloquium Mathematicum 137 (2014), 7-26 MSC: Primary 16E05; Secondary 13C60. DOI: 10.4064/cm137-1-2

Abstract

Given a semiperfect two-sided noetherian ring $\varLambda $, we study two subcategories $\mathcal {A}_k(\varLambda )=\{M\in \mathrm {mod}\ \varLambda \mid \mathrm {Ext}_\varLambda ^j(\mathop {{\rm Tr}}M,\varLambda )=0\ (1\leq j\leq k)\}$ and $\mathcal {B}_k(\varLambda )=\{N\in \mathrm {mod}\ \varLambda \mid \mathrm {Ext}_\varLambda ^j(N,\varLambda )=0\ (1\leq j\leq k)\}$ of the category $\mathop {\rm mod} \varLambda $ of finitely generated right $\varLambda $-modules, where $\mathop {\rm Tr}M$ is Auslander's transpose of $M$. In particular, we give another convenient description of the categories $\mathcal {A}_{k}(\varLambda )$ and $\mathcal {B}_{k}(\varLambda )$, 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 $\varLambda $ is a two-sided noetherian semiperfect ring.

Authors

  • Noritsugu KameyamaInterdisciplinary Graduate School
    of Science and Technology
    Shinshu University
    3-1-1 Asahi, Matsumoto
    Nagano, 390-8621, Japan
    e-mail
  • Yuko KimuraInterdisciplinary Graduate School
    of Science and Technology
    Shinshu University
    3-1-1 Asahi, Matsumoto
    Nagano, 390-8621, Japan
    e-mail
  • Kenji NishidaDepartment of Mathematical Sciences
    Shinshu University
    3-1-1 Asahi, Matsumoto
    Nagano, 390-8621, Japan
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image