1. Wakamatsu tilting modules with finite injective dimension
- Creator:
- Zhao, Guoqiang and Yin, Lirong
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Wakamatsu tilting module, $\omega $-$k$-torsionfree module, $\mathcal {X}$-resolution dimension, injective dimension, and $\omega $-torsionless property
- Language:
- English
- Description:
- Let $R$ be a left Noetherian ring, $S$ a right Noetherian ring and $_R\omega $ a Wakamatsu tilting module with $S={\rm End}(_R\omega )$. We introduce the notion of the $\omega $-torsionfree dimension of finitely generated $R$-modules and give some criteria for computing it. For any $n\geq 0$, we prove that ${\rm l.id}_R(\omega ) = {\rm r.id}_S(\omega )\leq n$ if and only if every finitely generated left $R$-module and every finitely generated right $S$-module have $\omega $-torsionfree dimension at most $n$, if and only if every finitely generated left $R$-module (or right $S$-module) has generalized Gorenstein dimension at most $n$. Then some examples and applications are given.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public