Cyclic polynomials arising from the functional equation for Dickson polynomials

被引：0

作者：

Bayarmagnai, Gombodorj ^{[1
]}

Ganbat, Batmunkh ^{[1
]}

机构：

[1] Natl Univ Mongolia, Sch Arts & Sci, Dept Math, WWF9 6H6, Ulan Bator 14201, Mongolia

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2023年 / 22卷 / 10期

关键词：

Cyclic extension; Dickson polynomial; irreducible polynomial; EXTENSIONS; FAMILIES;

D O I：

10.1142/S0219498823502195

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：13

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