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arXiv · 2608.10049

Virtually Gorenstein Artin algebras are weakly Gorenstein

Weiqing Li
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Abstract

We prove that all (possibly infinitely generated) semi-Gorenstein-projective modules over a virtually Gorenstein Artin algebra are Gorenstein projective. We also establish a new criterion for determining the projective (injective) dimensions of modules over virtually Gorenstein Artin algebras. This enables us to show the validities of the Auslander-Gorenstein Conjecture, the (Strong) Nakayama Conjecture and Tachikawa's First Conjecture for virtually Gorenstein Artin algebras. Finally, we prove that the Auslander-Reiten Conjecture holds for virtually Gorenstein Artin algebras of finite CM-type.

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Weiqing Li. 2026-08-10. Virtually Gorenstein Artin algebras are weakly Gorenstein. https://arxiv.org/abs/2608.10049

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