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)