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October, 2020 Monogenic Binomial Compositions
Joshua Harrington, Lenny Jones
Taiwanese J. Math. 24(5): 1073-1090 (October, 2020). DOI: 10.11650/tjm/200201

Abstract

We say a monic polynomial $f(x) \in \mathbb{Z}[x]$ of degree $n \geq 2$ is monogenic if $f(x)$ is irreducible over $\mathbb{Q}$ and $\{ 1, \theta, \theta^2, \ldots, \theta^{n-1} \}$ is a basis for the ring of integers of $\mathbb{Q}(\theta)$, where $f(\theta) = 0$. In this article, we investigate when a pair of polynomials $f(x) = x^n-a$ and $g(x) = x^m-b$ has the property that $f(x)$ and $f(g(x))$ are monogenic.

Citation

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Joshua Harrington. Lenny Jones. "Monogenic Binomial Compositions." Taiwanese J. Math. 24 (5) 1073 - 1090, October, 2020. https://doi.org/10.11650/tjm/200201

Information

Received: 6 November 2019; Revised: 24 January 2020; Accepted: 5 February 2020; Published: October, 2020
First available in Project Euclid: 11 February 2020

MathSciNet: MR4152656
Digital Object Identifier: 10.11650/tjm/200201

Subjects:
Primary: 11R04
Secondary: 11R09

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 5 • October, 2020
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