The Indecomposable K3 of Fields

In this note, we describe an extension of Hubert's Theorem 90 for K2 of fields to the relative K<i of semilocal PID's containing a field. Most of the results for K2 of fields proven in [M-S and S] then carry over to the relative K% of semilocal PID's containing a field, e.g. computation of the torsion subgroup, and the norm residue isomorphism. Applying this to the semilocal ring of {0,1} in A^, for a field E, gives a computation of the torsion and co-torsion in K3{Ey :=K3{E)/K^(E).