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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Compatible valuations and generalized Milnor $K$-theory
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by Ido Efrat PDF
Trans. Amer. Math. Soc. 359 (2007), 4695-4709 Request permission

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
  • 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
  • © Copyright 2007 American Mathematical Society
  • 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
  • MathSciNet review: 2320647