<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We study some factorization properties for univariate polynomials with coefficients in a discrete valuation domain (<italic>A,v</italic>). We use some properties of the Newton index of a polynomial <math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mi>F</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>d</mi></msubsup><mrow><msub><mi>a</mi><mi>i</mi></msub><msup><mi>X</mi><mrow><mi>d</mi><mo>-</mo><mi>i</mi></mrow></msup><mo>∈</mo><mtext> </mtext><mi>A</mi><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow></mrow></mrow></math> to deduce conditions on <italic>v</italic>(<italic>a<sub>i</sub></italic>) that allow us to find some information on the degree of the factors of <italic>F</italic>.</p></abstract>

We study some factorization properties for univariate polynomials with coefficients in a discrete valuation domain (A,v). We use some properties of the Newton index of a polynomial F(X)=∑i=0daiXd-i∈ A[X] to deduce conditions on v(ai) that allow us to find some information on the degree of the factors of F.

On the Factorization of Polynomials Over Discrete Valuation Domains

Department of Theoretical Physics and Mathematics, University of Bucharest Bdul M. Kogălniceanu 36–46, Bucharest, Romania

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the Factorization of Polynomials Over Discrete Valuation Domains"}

We study some factorization properties for univariate polynomials with coefficients in a discrete valuation domain (A,v). We use some properties of the Newton...

On the Factorization of Polynomials Over Discrete Valuation Domains

Published Online: Dec 10, 2014

Page range: 273 - 280

Received: Nov 01, 2013

Accepted: Nov 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0023

Keywords
irreducible polynomials, valuation, Newton polygon

© 2014 Doru Ştefănescu

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the Factorization of Polynomials Over Discrete Valuation Domains

Published Online: Dec 10, 2014

Page range: 273 - 280

Received: Nov 01, 2013

Accepted: Nov 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0023

Keywordsirreducible polynomials, valuation, Newton polygon

© 2014 Doru Ştefănescu

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
irreducible polynomials, valuation, Newton polygon