Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T05:22:57.721Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalized fundamental principle

Part of: Topological fields

Published online by Cambridge University Press:  26 February 2010

Sudesh K. Khanduja  and
Jayanti Saha
Sudesh K. Khanduja
Affiliation:
Center for Advanced Study in Mathematics, Panjab University, Chandigarh 160014, India. e-mail: [email protected]
Jayanti Saha
Affiliation:
Center for Advanced Study in Mathematics, Panjab University, Chandigarh 160014, India.
Get access

Abstract

Let ν be a rank 1 henselian valuation of a field K having unique extension ῡ to an algebraic closure of K. For any subextension L/K of /K, let G (L), Res (L) denote respectively the value group and the residue field of the valuation obtained by restricting ῡ to L. If a∈\K define

MSC classification

Secondary: 12J10: Valued fields
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 83 - 92
Copyright
Copyright © University College London 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Alexandru, V., Popescu, N. and Zaharescu, A.A theorem on characterization of residual transcendental extensions of a valuation. J. Math. Kyoto Univ., 28 (1988), 579–582.Google Scholar
2.Ax, J.Zeros of polynomials over local fields–the Galois action. J. Algebra, 15 (1970), 417–428.CrossRefGoogle Scholar
3.Bourbaki, N.. Commutative Algebra, Chapter 6, Valuations. (Hermann Publishers in Arts and Science, (1972).Google Scholar
4.Endler, O.. Valuation Theory (Springer-Verlag, New York, (1972).CrossRefGoogle Scholar
5.Khanduja, S. K.On a result of James. Ax. J. Algebra, 172 (1995), 147–151.CrossRefGoogle Scholar
6.Kuhlmann, F. V... Henselian function fields and tame fields (Manuscript, 1990.Google Scholar
7.Ohm, J.The henselian defect for valued function fields. Proc. Amer. Math. Soc., 107 (1989), 299–307.CrossRefGoogle Scholar
8.Ohm, J. and Matignon, M.Simple transcendental extensions of valued fields–III; The uniqueness property. J. Math. Kyoto Univ., 30 (1990), 347–365.Google Scholar
9.Popescu, N. and Zaharescu, A.On the structure of irreducible polynomials over local fields. Number Theory, 52 (1995), 98–118.Google Scholar