On the Wakamatsu tilting conjecture

2024/07/08 by Kamran Divaani-Aazar, Divaani-Aazar, Kamran, Ali Mahin Fallah +3
Mathematics · #Advanced Topics in Algebra #Advanced Algebra and Geometry #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2407.06353

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.

Related

• Equivalence classes of Wakamatsu tilting modules and preenveloping and precovering subcategories
• Cotilting invariance of the Auslander-Reiten conjecture
• Generalized tilting modules with finite injective dimension
• The Auslander-Reiten conjecture for Gorenstein rings
• Auslander--Reiten conjecture for normal rings