On stable equivalences of module subcategories over a semiperfect noetherian ring

Noritsugu Kameyama¹ ; Yuko Kimura¹ ; Kenji Nishida²

¹ Interdisciplinary Graduate School of Science and Technology Shinshu University 3-1-1 Asahi, Matsumoto Nagano, 390-8621, Japan
² Department of Mathematical Sciences Shinshu University 3-1-1 Asahi, Matsumoto Nagano, 390-8621, Japan

Colloquium Mathematicum, Tome 137 (2014) no. 1, pp. 7-26.

Résumé

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.

Détail

DOI : 10.4064/cm137-1-2

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