Taiwanese Journal of Mathematics

Monogenic Binomial Compositions

Joshua Harrington and Lenny Jones

Advance publication

This article is in its final form and can be cited using the date of online publication and the DOI.

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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.

Article information

Source
Taiwanese J. Math., Advance publication (2020), 18 pages.

Dates
First available in Project Euclid: 11 February 2020

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1581390013

Digital Object Identifier
doi:10.11650/tjm/200201

Subjects
Primary: 11R04: Algebraic numbers; rings of algebraic integers
Secondary: 11R09: Polynomials (irreducibility, etc.)

Keywords
monogenic irreducible composition

Citation

Harrington, Joshua; Jones, Lenny. Monogenic Binomial Compositions. Taiwanese J. Math., advance publication, 11 February 2020. doi:10.11650/tjm/200201. https://projecteuclid.org/euclid.twjm/1581390013


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