In this paper we discuss the problem to carry over the well-known Minkowski-Hasse local-global principle to the context of an infinite algebraic extension of the rationals or the rational function fields ????q(x) over finite fields. Applying this result we give a new proof of the elementary type conjecture for Witt rings of infinite algebraic extensions of global fields. This generalizes a result of I. Efrat [Ef] who proved, using Galois cohomology methods, a similar fact for algebraic extensions of the rationals.
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Vol. 12 (1998)
Published: 1998-09-30
10.2478/amsil
English