Absence of torsion for NK_1(R) over associative rings

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.

💡 Research Summary

The paper addresses the torsion problem for the nil‑K₁ group NK₁(R) over associative (not necessarily commutative) rings with identity. The classical result, due to C. Weibel, states that for a commutative ring R with identity, if a natural number k satisfies kR = R (i.e., k is a unit in R), then the special K₁ group SK₁(R