关于若松倾斜猜想

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2025-07-18 DOI:10.1007/s00013-025-02147-5

Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi

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引用次数: 0

摘要

设R是一个有恒等式的结合环。我们证明了广义Auslander-Reiten猜想隐含了Wakamatsu倾斜猜想。进一步证明了任何具有有限射影维且张量忠实的若松倾斜r模都是射影模。利用这一结果，我们在两种情况下证明了R的Wakamatsu倾斜猜想的有效性：当R是左Artinian局部环或当它是交换Artinian环上有限群G的群环时。

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On the Wakamatsu tilting conjecture

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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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.