Relations for Grothendieck groups of Gorenstein rings

Published 22 Apr 2016 in math.AC and math.RA | (1604.06530v1)

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

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