Khanduja, Sudesh K.
(1991)
*Prolongations of valuations to simple transcendental extensions with given residue field and value group*
Mathematika, 38
(02).
pp. 386-390.
ISSN 0025-5793

Full text not available from this repository.

Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1112/S0025579300006732

## Abstract

Let K_{0}(x) be a simple transcendental extension of a field K_{0}, υ_{0} be a valuation of K_{0} with value group G_{0} and residue field K_{0}. Suppose G_{0}⊆G_{1}⊆G is an inclusion of totally ordered abelian groups with [G_{1}: G_{0}] <∞such that G is the direct sum of G_{1} and an infinite cyclic group. It is proved that there exists an (explicitly constructible) valuation υ of K_{0}(x) extending υ_{0} such that the value group of υ is G and its residue field is k, where k is a given finite extension of k_{0}. This is analogous to a result of Matignon and Ohm [2, Corollary 3.2] for residually non-algebraic prolongations of υ_{0} to K_{0}(x).

Item Type: | Article |
---|---|

Source: | Copyright of this article belongs to University College London. |

Keywords: | 12f20: Field Theory and Polynomial; Field Extensions; Transcendental Extensions |

ID Code: | 69900 |

Deposited On: | 17 Nov 2011 03:37 |

Last Modified: | 17 Nov 2011 03:37 |

Repository Staff Only: item control page