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Compatible valuations and generalized Milnor $ K$-theory


Author: Ido Efrat
Journal: Trans. Amer. Math. Soc. 359 (2007), 4695-4709
MSC (2000): Primary 19F99; Secondary 12J15, 19C99, 12J99
DOI: https://doi.org/10.1090/S0002-9947-07-04132-3
Published electronically: April 24, 2007
MathSciNet review: 2320647
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Abstract: Given a field $ F$ and a subgroup $ S$ of $ F^{\times }$ there is a minimal group $ S\leq H_{S}\leq F^{\times }$ for which there exists an $ S$-compatible valuation whose units are contained in $ H_{S}$. Assuming that $ S$ has finite index in $ F^{\times }$ and contains $ (F^{\times })^{p}$ for $ p$ prime, we describe $ H_{S}$ in computable $ K$-theoretic terms.


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Additional Information

Ido Efrat
Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel
Email: efrat@math.bgu.ac.il

DOI: https://doi.org/10.1090/S0002-9947-07-04132-3
Received by editor(s): March 24, 2005
Published electronically: April 24, 2007
Additional Notes: This research was supported by the Israel Science Foundation grant No. 8008/02–1
Article copyright: © Copyright 2007 American Mathematical Society

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