Relations for Grothendieck groups of Gorenstein rings

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.

arXiv comment4 pages

References in corpus (1)

• Consequences of the existence of Auslander-Reiten triangles with applications to perfect complexes for self-injective algebras

Cited by in corpus (1)

• Syzygies of Cohen-Macaulay modules and Grothendieck groups