Journal of Prime Research in Mathematics

Algebraic integers of pure sextic extensions

Antonio Aparecido de Andrade\(^{1,*}\), Linara St´efani Facini\(^1\),Livea Cichito Esteves\(^1\)

\(^a\) 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


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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.


Algebraic number field, algebraic number integer, pure sextic extension.