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## On stable equivalences of module subcategories over a semiperfect noetherian ring

### Tom 137 / 2014

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

#### Streszczenie

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.

#### Autorzy

of Science and Technology
Shinshu University
3-1-1 Asahi, Matsumoto
Nagano, 390-8621, Japan
e-mail
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

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