Relations for Grothendieck groups of Gorenstein rings
Commutative Algebra
2016-04-26 v1 Rings and Algebras
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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Cite
@article{arxiv.1604.06530,
title = {Relations for Grothendieck groups of Gorenstein rings},
author = {Naoya Hiramatsu},
journal= {arXiv preprint arXiv:1604.06530},
year = {2016}
}
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4 pages