Abstract
$\tau $-rigid modules are essential in the $\tau $-tilting theory introduced by Adachi, Iyama and Reiten. In this paper, we give equivalent conditions for Iwanaga-Gorenstein algebras with self-injective dimension at most one in terms of $\tau $-rigid modules. We show that every indecomposable module over iterated tilted algebras of Dynkin type is $\tau $-rigid. Finally, we give a $\tau $-tilting theorem on homological dimension which is an analog to that of classical tilting modules.
Citation
Zongzhen Xie. Libo Zan. Xiaojin Zhang. "Three results for $\tau $-rigid modules." Rocky Mountain J. Math. 49 (8) 2791 - 2808, 2019. https://doi.org/10.1216/RMJ-2019-49-8-2791
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