Bloch-Wigner theorem over rings with many units II

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.