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arXiv · 1604.06530

Relations for Grothendieck groups of Gorenstein rings

Naoya Hiramatsu
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Abstract

We consider the converse of the Butler, Auslander-Reiten's Theorem which is on the relations for Grothendieck groups. We show that a Gorenstein ring is of finite representation type if the Auslander-Reiten sequences generate the relations for Grothendieck groups. This gives an affirmative answer of the conjecture due to Auslander.

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Naoya Hiramatsu. 2016-04-22. Relations for Grothendieck groups of Gorenstein rings. https://arxiv.org/abs/1604.06530

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