On prolongations of rank one discrete valuations

Fadil, Lhoussain El

doi:10.14712/1213-7243.2019.017

Commentationes Mathematicae Universitatis Carolinae

2019

DOI: 10.14712/1213-7243.2019.017

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On prolongations of rank one discrete valuations

Lhoussain El Fadil¹

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz

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2022

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On the Irreducible Factors of a Polynomial and Applications to Extensions of Absolute Values

Fadil¹,

Faris²

2022

Recent Advances in Polynomials

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Polynomial factorization over a field is very useful in algebraic number theory, in extensions of valuations, etc. For valued field extensions, the determination of irreducible polynomials was the focus of interest of many authors. In 1850, Eisenstein gave one of the most popular criterion to decide on irreducibility of a polynomial over Q. A criterion which was generalized in 1906 by Dumas. In 2008, R. Brown gave what is known to be the most general version of Eisenstein-Schönemann irreducibility criterion. Thanks to MacLane theory, key polynomials play a key role to extend absolute values. In this chapter, we give a sufficient condition on any monic plynomial to be a key polynomial of an absolute value, an irreducibly criterion will be given, and for any simple algebraic extension L=Kα, we give a method to describe all absolute values of L extending ∣∣, where K is a discrete rank one valued field.

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On the Irreducible Factors of a Polynomial and Applications to Extensions of Absolute Values

Fadil¹,

Faris²

2022

Recent Advances in Polynomials

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show abstract

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On prolongations of rank one discrete valuations

Cited by 1 publication

References 7 publications

On the Irreducible Factors of a Polynomial and Applications to Extensions of Absolute Values

On the Irreducible Factors of a Polynomial and Applications to Extensions of Absolute Values

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