# The stable rank of arithmetic orders in division algebras – an elementary approach

### Joachim Schwermer

Universität Wien, Austria### Ognjen Vukadin

Universität Wien, Austria

## Abstract

A well-known theorem of Bass implies that $2$ defines a stable range for an arithmetic order in a finite-dimensional semisimple algebra over an algebraic number field. The purpose of this note is to provide an independent and elementary proof of this fact for arithmetic orders contained in a finite-dimensional division algebra over an algebraic number field.

## Cite this article

Joachim Schwermer, Ognjen Vukadin, The stable rank of arithmetic orders in division algebras – an elementary approach. Enseign. Math. 57 (2011), no. 1, pp. 155–163

DOI 10.4171/LEM/57-1-7