On stable equivalences of module subcategories over a semiperfect noetherian ring
Tom 137 / 2014
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.
