Prime ideals of the Witt ring

In this chapter we determine minimal prime ideals of the Witt ring W(K) and show that they are intimately related to the orderings of the field K. This relationship is one of the most fundamental features of the theory of Witt rings. The minimal prime ideals are then used to give a completely satisfactory description of the elements of special types in Witt rings (nilpo- tent, torsion, units, zero divisors and idempotents). The deepest of these results is the characterization of torsion elements known as Pfister’s local–global principle.