POLYNOMIALS ANNIHILATING THE WITT RING

Let F be a non-formally real field of characteristic not 2 and let W(F ) be the Witt ring of F. In certain cases generators for the annihilat or ideal A(F) = {f(X) is an element of Z[X] \ f(phi) = 0 for all phi i s an element of W(F)} are determined. Also the primary decomposition o f A(F) is given. For formally real fields F, as an analogue the primar y decomposition of A(t)(F) = {f(X) is an element of Z[X] \ f(phi) = 0 for all phi is an element of W-t(F)}, where W-t(F) is the torsion part of the Witt group, is obtained.