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The map of the Witt ring of a domain into the Witt ring of its field of fractions

Authors: Thomas C. Craven, Alex Rosenberg and Roger Ware
Journal: Proc. Amer. Math. Soc. 51 (1975), 25-30
MSC: Primary 13K05
MathSciNet review: 0384789
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Abstract: Let $ R$ be an integral domain with field of fractions $ K$. This paper studies the kernel of the map $ W(R) \to W(K)$, where $ W$ is the Witt ring functor. In case $ R$ is regular and noetherian, it is shown that the kernel is a nilideal. The kernel is zero if $ R$ is a complete regular local noetherian ring with 2 a unit. Examples are given to show that the regularity assumptions are needed.

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Article copyright: © Copyright 1975 American Mathematical Society