Cyclic polynomials arising from the functional equation for Dickson polynomials
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Published:2022-07-02
Issue:
Volume:
Page:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Bayarmagnai Gombodorj1,
Ganbat Batmunkh1
Affiliation:
1. Department of Mathematics, School of Arts and Sciences, National University of Mongolia, WWF9+6H6, Ulaanbaatar 14201, Ulan Bator, Mongolia
Abstract
In this paper, we study algebraic properties of a family of certain polynomials arising from the functional equation for Dickson polynomials. We see that the roots and discriminants of those polynomials have very simple expressions, and each polynomial is cyclic. Further, we provide an irreducibility criterion analogous to the well-known criterion of Vahlen-Capelli. We finish the paper by showing that any cyclic extension of a certain field comes from a member of the family.
Funder
National University of Mongolia
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory