Absence of torsion for NK_1(R) over associative rings

Abstract

When R is a commutative ring with identity, and if k ∈ ℕ, with kR = R, then it was shown in [C. Weibel, Mayer–Vietoris Sequence and Module Structure on NK0, Lecture Notes in Mathematics, Vol. 854 (Springer, 1981), pp. 466–498] that SK1(R[X]) has no k-torsion. We prove this result for any associative ring R with identity in which kR = R.