English

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.

Keywords

Cite

@article{arxiv.1604.06530,
  title  = {Relations for Grothendieck groups of Gorenstein rings},
  author = {Naoya Hiramatsu},
  journal= {arXiv preprint arXiv:1604.06530},
  year   = {2016}
}

Comments

4 pages