Báyer, Pilar Quadratic forms over totally p-adic fields. (Spanish) Zbl 0574.10027 Proc. XIIth annu. Meet. Spanish mathematicians, Málaga 1976, 25-32 (1983). [For the entire collection see Zbl 0535.00006.] Let K be a field of numbers and \(P\neq \emptyset\) a finite set of prime elements of K. Then the totally P-adic field \(K_ P\) over K is formed by all finite extensions of K with the property that the elements of P decompose completely. The paper gives a characterization of the different quadratic forms over \(K_ P\) and investigates the Witt ring \(W(K_ P)\) of \(K_ P\). It turns out that \(W(K_ P)\) is infinite. The additive group of \(W(K_ P)\) is described by means of the Clifford invariant. Reviewer: W.B.Müller MSC: 11E08 Quadratic forms over local rings and fields 11E16 General binary quadratic forms Keywords:totally P-adic field; quadratic forms; Witt ring; additive group; Clifford invariant Citations:Zbl 0535.00006 PDFBibTeX XML