Bloch–Wigner theorem over rings with many units

Abstract

The Bloch–Wigner theorem over an algebraically closed field F determines a connection between the third homology of SL2(F) and the group describing the nontrivial relations on the tensors of the form \({{x\otimes(1-x) (x \in F^\times \backslash \{1\})}}\). The purpose of this article is to provide a version of this theorem over rings with large number of unites, for examples semi-local rings with infinite residue fields.