Absence of torsion for NK_1(R) over associative rings

TL;DR

This paper extends Weibel's result on the absence of k-torsion in SK_1(R[X]) from commutative rings to all associative rings with identity where kR=R, broadening the applicability of the theorem.

Contribution

The paper generalizes Weibel's proof of no k-torsion in SK_1(R[X]) to include all associative rings with identity satisfying kR=R.

Findings

SK_1(R[X]) has no k-torsion for associative rings with identity where kR=R

The proof is extended beyond commutative rings to associative rings

The result applies to a broader class of rings, enhancing algebraic K-theory understanding.

Abstract

When R is a commutative ring with identity, and if k is a natural number with kR = R, then C. Weibel proved that SK_1(R[X]) has no k-torsion. We reprove his result for any associative ring R with identity in which kR = R.