Hölder absolute values are equivalent to classical ones
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- by E. Muñoz Garcia PDF
- Proc. Amer. Math. Soc. 127 (1999), 1967-1971 Request permission
Abstract:
We study generalized absolute values on a field or a commutative ring with unit element satisfying an approximate triangle inequality and an approximate multiplicative property. We prove that they are always Hölder equivalent to an absolute value. This implies geometric rigidity results for Lipschitz and Hölder deformations of metric rings.References
- Nicolas Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR 0360549
- A. Ostrowski, Über einige Lösungen der Funktionalgleichung $\varphi (x).\varphi (y)=\varphi (xy)$ Acta Mathematica, 41, 1917, p. 271-284.
- Dominic Welsh, Codes and cryptography, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1988. MR 959137
Additional Information
- E. Muñoz Garcia
- Affiliation: Department of Mathematics, University of California, Los Angeles, California 90024
- Email: munoz@math.ucla.edu
- Received by editor(s): June 25, 1997
- Received by editor(s) in revised form: October 14, 1997
- Published electronically: March 16, 1999
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1967-1971
- MSC (1991): Primary 12J20; Secondary 12J10, 16W80, 13J99
- DOI: https://doi.org/10.1090/S0002-9939-99-04758-9
- MathSciNet review: 1487331