Stable range one for rings with central units
Rings and Algebras
2019-10-11 v1
Abstract
The purpose of this paper is to give a partial positive answer to a question raised by Khurana et al. as to whether a ring with stable range one and central units is commutative. We show that this is the case under any of the following additional conditions: is semiprime or is one-sided Noetherian or has unit-stable range or has classical Krull dimension or is an algebra over a field such that is uncountable and has only countably many primitive ideals or is affine and either has characteristic or has infinite transcendental degree over its prime subfield or is algebraically closed. However, the general question remains open.
Cite
@article{arxiv.1910.04410,
title = {Stable range one for rings with central units},
author = {Paula A. A. B. Carvalho and Christian Lomp and Jerzy Matczuk},
journal= {arXiv preprint arXiv:1910.04410},
year = {2019}
}