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REPRESENTING AN ELEMENT IN ${\mathbf{F} }_{q} [t] $ AS THE SUM OF TWO IRREDUCIBLES

Part of: Finite fields and commutative rings (number-theoretic aspects) Algebraic number theory: global fields

Published online by Cambridge University Press:  23 May 2013

Andreas O. Bender
Andreas O. Bender*
Affiliation:
Pohang Mathematics Institute, POSTECH, San 31 Hyoja-dong, Pohang 790-784, Republic of Korea email andreasobender@mac.com
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Abstract

A monic polynomial in ${\mathbf{F} }_{q} [t] $ of degree $n$ over a finite field ${\mathbf{F} }_{q} $ of odd characteristic can be written as the sum of two irreducible monic elements in ${\mathbf{F} }_{q} [t] $ of degrees $n$ and $n- 1$ if $q$ is larger than a bound depending only on $n$. The main tool is a sufficient condition for simultaneous primality of two polynomials in one variable $x$ with coefficients in ${\mathbf{F} }_{q} [t] $.

MSC classification

Secondary: 11R09: Polynomials (irreducibility, etc.) 11T55: Arithmetic theory of polynomial rings over finite fields

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Type
Research Article
Information
Mathematika , Volume 60 , Issue 1 , January 2014 , pp. 166 - 182
Copyright
Copyright © University College London 2013 

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