Relations for Grothendieck groups of Gorenstein rings

2016/04/22 by Naoya Hiramatsu, Hiramatsu, Naoya · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1604.06530

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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• Syzygies of Cohen-Macaulay modules and Grothendieck groups

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