We study the homomorphism W???? → WK between the Witt ring of a domain ???? and the Witt ring of its field of fractions K in the case when ???? is not integrally closed. We give sufficient conditions for the noninjectivity of this homomorphism by constructing nonzero elements in the kernel. In particular, when K is an algebraic number field and ???? is a nonmaximal order in K with even conductor, then the ring homomorphism W???? → WK is not injective.
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Vol. 21 (2007)
Published: 2007-09-28
10.2478/amsil
English