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Algebraic integers of pure sextic extensions

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Title: Algebraic integers of pure sextic extensions

Authors: Antonio Aparecido de Andrade, Linara St´efani Facini, Livea Cichito Esteves

Journal: Journal of Prime Research in Mathematics

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
Y 2020-07-01 2021-06-30

Publisher: Abdus Salam School of Mathematical Sciences, GC University

Country: Pakistan

Year: 2022

Volume: 18

Issue: 2

Language: English

Keywords: pure sextic extensionsalgebraic integers

Categories
Algebraic Number Theory (3) Field Extensions (1) Algebraic Integers (2) Pure Sextic Extensions (1) Number Fields (1)

Abstract

Let K = Q(θ), where θ = √6 d, be a pure sextic field with d ̸= 1 a square free integer. In this paper, we characterize completely whether {1, θ, . . . , θ5} is an integral basis of K or do not. When d ̸≡ ±1, ±17, ±10, −15, −11, −7, −3, 5, 13(mod 36) we prove that K has a power integral basis. Furthermore, for the other cases we present an integral basis.

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