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 v_{0} be a valuation of a field K_{0} with value group G_{0} and v be an extension of u0 to a simple transcendental
extension K_{0}{x) having value group G such that G/G_{0} is not a torsion group. In this paper we investigate
whether there exists teKJ,x)\K_{0} with v(t) non-torsion mod Go such that i> is the unique extension to K_{0}(x) of
its restriction to the subfield X_{0}(t). It is proved that the answer to this question is "yes" if v_{0} is henselian or if
v_{0} is of rank 1 with G_{0} 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)/(K_{0}, v_{0}).

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