On the arithmetic of the rational function field \(K(X)\)

Sarfraz Ahmad
School of Mathematical Sciences, GC Unversity, Lahore, 68-B, New Muslim Town,
Lahore, Pakistan.
Angel Popescu
Technical University of Civil Engineering, Bucharest, Romania.

\(^{1}\)Corresponding Author:sarfraz11@gmail.com

Copyright © 2006 Sarfraz Ahmad, Angel Popescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2006.

Abstract

Let \(K\) be a commutative field. In this paper we study the action of the automorphism group of the rational function field \(K(X)\) on the set of all valuations of \(K(X)\) which are trivial on \(K\). We apply this study in finding a classification of some simple algebraic extension of \(K\).

Keywords:

Valuation Theory, Algebraic Extensions, Automorphism, Action of groups.