## Taiwanese Journal of Mathematics

### Monogenic Binomial Compositions

#### 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

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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