Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T06:23:22.318Z Has data issue: false hasContentIssue false
  • English
  • Français

ALL NON-ARCHIMEDEAN NORMS ON K[X1, . . ., Xr]

Published online by Cambridge University Press:  30 July 2009

GHIOCEL GROZA ,
NICOLAE POPESCU  and
ALEXANDRU ZAHARESCU
GHIOCEL GROZA
Affiliation:
Department of Mathematics, Technical University of Civil Engineering, Lacul Tei 124, Sec.2, RO-020396 Bucharest, Romania e-mail: grozag@mail.utcb.ro
NICOLAE POPESCU
Affiliation:
Romanian Academy, Institute of Mathematics, P.O. Box 1-764, RO-70700Bucharest, Romania e-mail: Nicolae.Popescu@imar.ro
ALEXANDRU ZAHARESCU
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA e-mail: zaharesc@math.uiuc.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If K is a field with a non-trivial non-Archimedean absolute value (multiplicative norm) | |, we describe all non-Archimedean K-algebra norms on the polynomial algebra K[X1, . . . , Xr] which extend | |.

Keywords

11S7511C08
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 1 - 18
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Alexandru, V., Popescu, N. and Zaharescu, A., A theorem of characterization of residual transcendental extensions of a valuation, J. Math. Kyoto Univ. 28 (4) (1988), 579–592.Google Scholar
2.Alexandru, V., Popescu, N. and Zaharescu, A., All valuations on K(X), J. Math. Kyoto Univ. 30 (2) (1990), 281–296.Google Scholar
3.Alexandru, V., Popescu, N. and Zaharescu, A., Minimal pairs of definition of a residual transcendental extension of a valuation, J. Math. Kyoto Univ. 30 (2) (1990), 207–225.Google Scholar
4.Bourbaki, N., Algèbre commutative, Ch. VI Valuations (Hermann, Paris, 1964).Google Scholar
5.Cohen, I. S., On non-Archimedean normed spaces, Indag. Math. 10 (1948), 244–249.Google Scholar
6.Goldman, O. and Iwahori, N., The space of p-adic norms, Acta Math. 109 (1963), 137–177.CrossRefGoogle Scholar
7.Kuhlmann, F.-V., Value groups, residue fields and bad places of rational function fields, Trans. Amer. Math. Soc. 356 (11) (2004), 4559–4600.CrossRefGoogle Scholar
8.Monna, A. F., Sur les espaces linéaires normés I–IV, Indag. Math. 8 (1946), 643–660, 682–700.Google Scholar
9.Nagata, M., A theorem on valuation rings and its applications, Nagoya Math. J. 29 (1967), 85–91.CrossRefGoogle Scholar