Whitehead groups of exchange rings with primitive factors artinian

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.