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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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