Mathematica Bohemica, Vol. 146, No. 4, pp. 471-481, 2021
Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
Julio Pérez-Hernández, Mario Pineda-Ruelas
Received September 9, 2019. Published online February 11, 2021.
Abstract: If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ 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 $q{\mathcal O}_K$, where $q$ is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.
Keywords: ramification; cyclic quartic field; discriminant; index
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Affiliations: Julio Pérez-Hernández, Mario Pineda-Ruelas, Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Avenida San Rafael Atlixco No. 186, Col. Vicentina, CP 09340, Ciudad de México, Mexico, e-mail: galois60@gmail.com, mpr@xanum.uam.mx
