K2 of a ring

Summary

The group $K_2(R)$ of a ring $R$ is Milnor's second algebraic K-group. It is the kernel of the map from the Steinberg group to the group of elementary matrices. So it collects the relations among elementary matrices that are not consequences of the obvious ones. For a field it is generated by symbols $\set{a, b}$, and it is linked to reciprocity laws, to the Brauer group and to Galois cohomology.