Bloch-Wigner theorem over rings with many units II

TL;DR

This paper generalizes the Bloch-Wigner exact sequence to commutative rings with many units, extending Suslin's results over infinite fields, with a simpler proof leveraging homology of general linear groups.

Contribution

It provides a new, simpler proof of the Bloch-Wigner exact sequence for rings with many units, broadening the scope of previous results over fields.

Findings

Generalization of Bloch-Wigner exact sequence to rings with many units

Simplified proof approach using homology of GL groups

Extension of Suslin's results to a broader class of rings

Abstract

In this article we prove a generalization of the Bloch-Wigner exact sequence over commutative rings with many units. When the ring is a domain, we get a generalization of Suslin's Bloch-Wigner exact sequence over infinite fields. Our proof is different and is easier, even in its general form. But nevertheless we use some of Suslin's results which relates the Bloch group of the ring to the third homology group of the general linear group of the ring. From there we take an easier path.