English

Every abelian group is the class group of a simple Dedekind domain

Rings and Algebras 2017-06-13 v2

Abstract

A classical result of Claborn states that every abelian group is the class group of a commutative Dedekind domain. Among noncommutative Dedekind prime rings, apart from PI rings, the simple Dedekind domains form a second important class. We show that every abelian group is the class group of a noncommutative simple Dedekind domain. This solves an open problem stated by Levy and Robson in their recent monograph on hereditary Noetherian prime rings.

Keywords

Cite

@article{arxiv.1505.00608,
  title  = {Every abelian group is the class group of a simple Dedekind domain},
  author = {Daniel Smertnig},
  journal= {arXiv preprint arXiv:1505.00608},
  year   = {2017}
}

Comments

17 pages; final version (no significant changes)