Monogenic Cyclic Quartic Trinomials

2024/04/27 by Lenny Jones, Jones, Lenny
Mathematics · Engineering · #Mathematics and Applications #Algebraic and Geometric Analysis #Advanced Theoretical and Applied Studies in Material Sciences and Geometry

paper · pdf · doi:10.48550/arxiv.2404.17869

Abstract

A monic polynomial f(x)∈ \mathbb Z[x] of degree N is called monogenic if f(x) is irreducible over \mathbb Q and \1,θ,θ²,… ,θ^N-1\ is a basis for the ring of integers of \mathbb Q(θ), where f(θ)=0. In this brief note, we prove that there exist exactly three distinct monogenic trinomials of the form x⁴+bx²+d whose Galois group is the cyclic group of order 4.

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