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
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
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.