Integral bases and monogenity of pure fields

By Istv'an Ga'al, László Remete. 2017

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Abstract Let m be a square-free integer ( m ≠ 0 , ± 1 ). We show that the structure of the integral bases of the fields K = Q ( m n ) is periodic in m. For 3 ≤ n ≤ 9 we show that the period length is n 2 . We explicitly describe the integral bases, and for n = 3 , 4 , 5 , 6 , 8 we explicitly calculate the index forms of K. This enables us in many cases to characterize the monogenity of these fields. Using the explicit form of the index forms yields a new technic that enables us to derive new results on monogenity and to get several former results as easy consequences. For n = 4 , 6 , 8 we give an almost complete characterization of the monogenity of pure fields.

Subfields: Artificial Intelligence, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/297d59f086c0e4ef110b19768d5d58f58466918f