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A generalized fundamental principle

Published online by Cambridge University Press:  26 February 2010

Sudesh K. Khanduja
Affiliation:
Center for Advanced Study in Mathematics, Panjab University, Chandigarh 160014, India. e-mail: skhand@panjabuniv.chd.nic.in
Jayanti Saha
Affiliation:
Center for Advanced Study in Mathematics, Panjab University, Chandigarh 160014, India.
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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

Type
Research Article
Copyright
Copyright © University College London 1999

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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), 579582.Google Scholar
2.Ax, J.Zeros of polynomials over local fields–the Galois action. J. Algebra, 15 (1970), 417428.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), 147151.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), 299307.CrossRefGoogle Scholar
8.Ohm, J. and Matignon, M.Simple transcendental extensions of valued fields–III; The uniqueness property. J. Math. Kyoto Univ., 30 (1990), 347365.Google Scholar
9.Popescu, N. and Zaharescu, A.On the structure of irreducible polynomials over local fields. Number Theory, 52 (1995), 98118.Google Scholar