Algebraic integers of pure sextic extensions

Authors

  • Antonio Aparecido de Andrade Department of Mathematics, S˜ao Paulo State University (Unesp), Institute of Biosciences, Humanites and Exact Sciences (Ibilce),Campus S˜ao Jos´e do Rio Preto, S˜ao Paulo, Brazil
  • Linara St´efani Facini Department of Mathematics, S˜ao Paulo State University (Unesp), Institute of Biosciences, Humanites and Exact Sciences (Ibilce),Campus S˜ao Jos´e do Rio Preto, S˜ao Paulo, Brazil
  • Livea Cichito Esteves Department of Mathematics, S˜ao Paulo State University (Unesp), Institute of Biosciences, Humanites and Exact Sciences (Ibilce),Campus S˜ao Jos´e do Rio Preto, S˜ao Paulo, Brazil.

Keywords:

Algebraic number field, algebraic number integer, pure sextic extension

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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Published

2022-12-31

Issue

Vol. 18 No. 2 (2022): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

Algebraic integers of pure sextic extensions. (2022). Journal of Prime Research in Mathematics, 18(2), 112 – 124. https://jprm.sms.edu.pk/index.php/jprm/article/view/201