Relations for Grothendieck groups of Gorenstein rings
classification
🧮 math.AC
math.RA
keywords
grothendieckgroupsrelationsauslander-reitengorensteinaffirmativeanswerauslander
read the original 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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