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RAMIFICATION IN NUMBER FIELDS GENERATED BY x^4+p x^2+p WITH p \neq 4+n^2 A RATIONAL PRIME

Year: 2025

Type: article

Abstract: If is the splitting field of the polynomial and is a rational prime, then we have , where is the dihedral group of order 8 . We calculate the discriminant of without knowing any integral basis of ; also, we obtain the explicit ramification of any rational prime such that . For this, we first study the ramification in the intermediate quartic field . We give generators of each ramified rational prime. In some cases, we can make use of Dedekind's Theorem; in other cases, we use the relative extension theory.

Source: JP Journal of Algebra Number Theory and Applications

DOI: 10.17654/0972555525019

Authors: Julio Pérez-Hernández, Mario Pineda-Ruelas

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Consejo Nacional de Ciencia y Tecnología

OpenAlex ID: W4410714540

FWCI:

Cites: 1

Cited by:

Related to: 10