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Keywords:
ramification; cyclic quartic field; discriminant; index
ramification; cyclic quartic field; discriminant; index
Summary:
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.
References:
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