Rocky Mountain Journal of Mathematics

Three results for $\tau $-rigid modules

Zongzhen Xie, Libo Zan, and Xiaojin Zhang

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$\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.

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Rocky Mountain J. Math., Volume 49, Number 8 (2019), 2791-2808.

First available in Project Euclid: 31 January 2020

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Zentralblatt MATH identifier

Primary: 16G10: Representations of Artinian rings 16E10.

$\tau $-rigid module projective dimension tilted algebra


Xie, Zongzhen; Zan, Libo; Zhang, Xiaojin. Three results for $\tau $-rigid modules. Rocky Mountain J. Math. 49 (2019), no. 8, 2791--2808. doi:10.1216/RMJ-2019-49-8-2791.

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