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Hölder absolute values are equivalent
to classical ones
Author:
E. Muñoz Garcia
Journal:
Proc. Amer. Math. Soc. 127 (1999), 1967-1971
MSC (1991):
Primary 12J20; Secondary 12J10, 16W80, 13J99
Posted:
March 16, 1999
MathSciNet review:
1487331
Full-text PDF Free Access
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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.
- [Bou]
Nicolas
Bourbaki, Elements of mathematics. Commutative algebra,
Hermann, Paris, 1972. Translated from the French. MR 0360549
(50 #12997)
- [Os]
A. Ostrowski, Über einige Lösungen der Funktionalgleichung
 Acta Mathematica, 41, 1917, p. 271-284.
- [We]
Dominic
Welsh, Codes and cryptography, Oxford Science Publications,
The Clarendon Press Oxford University Press, New York, 1988. MR 959137
(89i:94001)
- [Bou]
- N. Bourbaki, Commutative algebra Elements of Mathematics, chapter VI, section 6.1, Addison-Wesley, 1972. MR 50:12997
- [Os]
- A. Ostrowski, Über einige Lösungen der Funktionalgleichung Acta Mathematica, 41, 1917, p. 271-284.
- [We]
- D. Welsh, Codes and cryptography Oxford Science Publications, 1988. MR 89i:94001
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Additional Information
E. Muñoz Garcia
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90024
Email:
munoz@math.ucla.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04758-9
PII:
S 0002-9939(99)04758-9
Keywords:
Valuations,
Ostrowski's Theorem,
H\"{o}lder deformations,
metric spaces
Received by editor(s):
June 25, 1997
Received by editor(s) in revised form:
October 14, 1997
Posted:
March 16, 1999
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 1999 American Mathematical Society
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