RELATIONS FOR GROTHENDIECK GROUPS OF GORENSTEIN RINGS

Naoya Hiramatsu

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.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

145

2

559

562

10.1090/proc/13255

https://doi.org/10.1090/proc/13255
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