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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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A rigidity property for the set of all characters induced by valuations
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by Robert Bieri and John R. J. Groves PDF
Trans. Amer. Math. Soc. 294 (1986), 425-434 Request permission

Abstract:

If $K$ is a field and $G$ a finitely generated multiplicative subgroup of $K$ then every real valuation on $K$ induces a character $G \to {\mathbf {R}}$. It is known that the set $\Delta (G) \subseteq {{\mathbf {R}}^n}$ of all characters induced by valuations is polyhedral. We prove that $\Delta (G)$ satisfies a certain rigidity property and apply this to give a new and conceptual proof of the Brewster-Roseblade result [4] on the group of automorphisms of $K$ stabilizing $G$.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 425-434
  • MSC: Primary 16A27; Secondary 12J20, 13A18
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825713-6
  • MathSciNet review: 825713