Year: 2026
Type: preprint
Abstract: The study of monogenic polynomials is a classical problem in algebraic number theory. Existing criteria for deciding whether a polynomial is monogenic typically rely on discriminant computations together with methods such as Dedekind's criterion, Newton polygons, or valuation-theoretic techniques. In this paper, we develop a general local criterion for the $p$-maximality of orders generated by roots of arbitrary monic irreducible polynomials. As an application, we apply this to irreducible polynomials of the type $f(X)=X^n+A(BX+1)^m,$ where $1\le m
Source: arXiv (Cornell University)
Authors: Karatarakis, Michail, Kaur, Sumandeep
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214928663