Journal of Prime Research in Mathematics

# On the arithmetic of the rational function field $$K(X)$$

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

### 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.