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

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

Authors: Sarfraz Ahmad, Angel Popescu

Journal: Journal of Prime Research in Mathematics

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
Y 2020-07-01 2021-06-30

Publisher: Abdus Salam School of Mathematical Sciences, GC University

Country: Pakistan

Year: 2006

Volume: 1

Issue: 1

Language: English

Categories
Algebraic Geometry (13) Fields (4) Rational Functions (3) Number Theory (108) Mathematics (5170)

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 \(K\).

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