Khanduja, Sudesh K. ; Jayanti , Saha
(1996)
*A uniqueness problem in valued function fields of conics*
Bulletin of the London Mathematical Society, 28
(5).
pp. 455-462.
ISSN 0024-6093

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Official URL: http://blms.oxfordjournals.org/content/28/5/455.sh...

Related URL: http://dx.doi.org/10.1112/blms/28.5.455

## Abstract

Let v_{0} be a valuation of a field K_{0} with value group G_{0}. Let K be a function field of a conic over K_{0}, and let v be an extension of v_{0} to K with value group G such that G/G_{0} is not a torsion group. Suppose that either (K_{0}, v_{0}) is henselian or v_{0} is of rank 1, the algebraic closure of K_{0} in K is a purely inseparable extension of K_{0}, and G_{0} is a cofinal subset of G. In this paper, it is proved that there exists an explicitly constructible element t in K, with v(t) non-torsion modulo G_{0} such that the valuation of K_{0}(t), obtained by restricting v, has a unique extension to K. This generalizes the result proved by Khanduja in the particular case, when K is a simple transcendental extension of K_{0} (compare [4]). The above result is an analogue of a result of Polzin proved for residually transcendental extensions [8].

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ID Code: | 69948 |

Deposited On: | 19 Nov 2011 10:22 |

Last Modified: | 19 Nov 2011 10:22 |

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