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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The map of the Witt ring of a domain into the Witt ring of its field of fractions
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by Thomas C. Craven, Alex Rosenberg and Roger Ware PDF
Proc. Amer. Math. Soc. 51 (1975), 25-30 Request permission


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.
    N. Bourbaki, Éléments de mathématique. Fasc. XXXI. Chap. 7, Algèbre commutative, Actualités Sci. Indust., no. 1314, Hermann, Paris, 1965. MR 41 #5339. T. C. Craven, Witt rings and orderings of fields, Ph. D. Thesis, Cornell University, Ithaca, N. Y., 1973.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 25-30
  • MSC: Primary 13K05
  • DOI:
  • MathSciNet review: 0384789