International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 7, Pages 393-398
doi:10.1155/S0161171201005464
Whitehead groups of exchange rings with primitive factors artinian
1Department of Mathematics, Hunan Normal University, Changsha 410006, China
2Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China
Received 8 October 2000
Copyright © 2001 Huanyin Chen and Fu-an Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We show that if R is an exchange ring with primitive factors artinian then K1(R)≅U(R)/V(R), where U(R) is the group of units of R and V(R) is the subgroup generated by {(1+ab)(1+ba)−1|a,b∈R with 1+ab∈U(R)}. As a corollary, K1(R) is the abelianized group of units of R if 1/2∈R.