A Note on Abelian Monogenic Trinomials
Year: 2026
Type: article
Abstract: An abelian monogenic polynomial f ( x ) ∈ Z [ x ] $f(x)\in {\mathbb Z}[x]$ f left parenthesis x right parenthesis element of double struck upper Z left bracket x right bracket is a monic polynomial of degree N ≥ 2 $N\ge 2$ upper N greater than or equals 2 that is irreducible over Q ${\mathbb Q}$ double struck upper Q , such that the Galois group of f ( x ) $f(x)$ f left parenthesis x right parenthesis over Q ${\mathbb Q}$ double struck upper Q is abelian, and { 1 , θ , θ 2 , … , θ N − 1 } $\{1,\theta ,\theta ^2,\ldots ,\theta ^{N-1}\}$ StartSet 1 comma theta comma theta squared comma ellipsis comma theta Superscript upper N minus 1 Baseline EndSet is a basis for the ring of integers of Q ( θ ) ${\mathbb Q}(\theta )$
Author: LENNY JONES
Institution: Shippensburg University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
OpenAlex ID: W7170139648