International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 7, Pages 393-398

Whitehead groups of exchange rings with primitive factors artinian

Huanyin Chen1 and Fu-an Li2

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.


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,bRwith1+abU(R)}. As a corollary, K1(R) is the abelianized group of units of R if 1/2R.