2021 MONOGENICALLY STABLE POLYNOMIALS
Lenny Jones
Author Affiliations +
Albanian J. Math. 15(2): 85-98 (2021). DOI: 10.51286/albjm/1635847634

Abstract

A monic polynomial f(x)[x] is called stable if fn(x) is irreducible over for all n1, where fn(x) denotes the nth iterate of f(x). Regardless of whether f(x) is irreducible over , if there exists some monic g(x)[x] such that g(fn(x)) is irreducible over for all n1, we say that f(x) is g-stable. Many authors have studied such polynomials since Odoni first introduced this concept of stability in 1985. We extend these concepts here by adding the additional restriction of monogeneity. A monic polynomial f(x)[x] is defined to be monogenic if f(x) is irreducible over and 1,θ,θ2,,θdegf1 is a basis for the ring of integers of θ, where f(θ)=0. We say that f(x) is g-monogenically stable, if g(fn(x)) is monogenic for all n1, for some monic g(x)[x]. When g(x)=x, we simply say that f(x) is monogenically stable. In this article, we provide methods for constructing g-monogenically stable polynomials f(x), for various polynomials f(x) and g(x).

Citation

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Lenny Jones. "MONOGENICALLY STABLE POLYNOMIALS." Albanian J. Math. 15 (2) 85 - 98, 2021. https://doi.org/10.51286/albjm/1635847634

Information

Published: 2021
First available in Project Euclid: 11 July 2023

MathSciNet: MR4346263
zbMATH: 1490.11107
Digital Object Identifier: 10.51286/albjm/1635847634

Subjects:
Primary: 11R06 , 11R09 , 12F05

Keywords: irreducible polynomial , monogenic polynomial , stable polynomial

Rights: Copyright © 2021 Research Institute of Science and Technology (RISAT)

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Vol.15 • No. 2 • 2021
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