Stabilization theorem for the Milnor $K_2$-functor

A. A. Suslin ; M. S. Tulenbaev

Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 131-152

Résumé

Let $\Lambda$ be an associative ring. For every natural number $n$ there is a canonical homomorphism $\Psi_n\colon K_{2,n}(\Lambda)\to K_2(\lambda)$ where $K_2$ is the Milnor functor and $K_{2,n}(\lambda)$ the associated unstable $K$-group. Dennis and Vasershtein have proved that if $n$ is larger than the stable rank of $\Lambda$, $\Psi_n$is an epimorphism. It is proved in the article that if $n-1$ is greater than the stable rank of $\Lambda$, the homomorphism $\Psi_n$ is an isomorphism.