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Ramification in quartic cyclic number fields $K$ generated by $x^{4} + p x^{2} + p$

Julio Pérez-Hernández; Mario Pineda-Ruelas — 2021

Mathematica Bohemica

If $K$ is the splitting field of the polynomial $f (x) = x^{4} + p x^{2} + p$ and $p$ is a rational prime of the form $4 + n^{2}$ , we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q 𝒪_{K}$ , where $q$ is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.

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