A uniqueness problem in simple transcendental extensions of valued fields

Khanduja, Sudesh K. (1993) A uniqueness problem in simple transcendental extensions of valued fields Proceedings of the Edinburgh Mathematical Society, 37 . pp. 13-23. ISSN 0013-0915

Full text not available from this repository.

Official URL: http://journals.cambridge.org/production/action/cj...

Abstract

Let v0 be a valuation of a field K0 with value group G0 and v be an extension of u0 to a simple transcendental extension K0{x) having value group G such that G/G0 is not a torsion group. In this paper we investigate whether there exists teKJ,x)\K0 with v(t) non-torsion mod Go such that i> is the unique extension to K0(x) of its restriction to the subfield X0(t). It is proved that the answer to this question is "yes" if v0 is henselian or if v0 is of rank 1 with G0 a cofinal subset of the value group of v in the latter case, and that it is "no" in general. It is also shown that the affirmative answer to this problem is equivalent to a fundamental equality which relates some important numerical invariants of the extension (K, v)/(K0, v0).

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
ID Code:69892
Deposited On:17 Nov 2011 03:38
Last Modified:17 Nov 2011 03:38

Repository Staff Only: item control page