2019/10/10 by Carvalho, Paula A. A. B., Lomp, Christian, Matczuk, Jerzy
#16U60 #16U70 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1910.04410
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 R with stable range one and central units is commutative. We show that this is the case under any of the following additional conditions: R is semiprime or R is one-sided Noetherian or R has unit-stable range 1 or R has classical Krull dimension 0 or R is an algebra over a field K such that K is uncountable and R has only countably many primitive ideals or R is affine and either K has characteristic 0 or has infinite transcendental degree over its prime subfield or is algebraically closed. However, the general question remains open.