Relations for Grothendieck groups of Gorenstein rings

Hiramatsu, Naoya

doi:10.1090/proc/13255

Relations for Grothendieck groups of Gorenstein rings
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by Naoya Hiramatsu PDF

Proc. Amer. Math. Soc. 145 (2017), 559-562 Request permission

Abstract:

We consider the converse of the Butler, Auslander-Reiten Theorem, which concerns 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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