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arXiv · 2407.06353

On the Wakamatsu tilting conjecture

Kamran Divaani-Aazar·Ali Mahin Fallah·Massoud Tousi
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Abstract

Let R be an associative ring with identity. We establish that the generalized Auslander-Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any Wakamatsu tilting R-module of finite projective dimension that is tensorly faithful is projective. By utilizing this result, we show the validity of the Wakamatsu tilting conjecture for R in two cases: when R is a left Artinian local ring or when it is the group ring of a finite group G over a commutative Artinian ring.

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Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi. 2024-07-08. On the Wakamatsu tilting conjecture. https://arxiv.org/abs/2407.06353

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