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2019 Three results for $\tau $-rigid modules
Zongzhen Xie, Libo Zan, Xiaojin Zhang
Rocky Mountain J. Math. 49(8): 2791-2808 (2019). DOI: 10.1216/RMJ-2019-49-8-2791

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.

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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

Information

Published: 2019
First available in Project Euclid: 31 January 2020

zbMATH: 07163199
MathSciNet: MR4058350
Digital Object Identifier: 10.1216/RMJ-2019-49-8-2791

Subjects:
Primary: 16E10., 16G10

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 8 • 2019
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