Ramification in quartic cyclic number fields K generated by x 4 + p x 2 + p

Julio Pérez-Hernández; Mario Pineda-Ruelas

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 4, page 471-481
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Pérez-Hernández, Julio, and Pineda-Ruelas, Mario. "Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$." Mathematica Bohemica 146.4 (2021): 471-481. <http://eudml.org/doc/298278>.

@article{Pérez2021,
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.},
author = {Pérez-Hernández, Julio, Pineda-Ruelas, Mario},
journal = {Mathematica Bohemica},
keywords = {ramification; cyclic quartic field; discriminant; index},
language = {eng},
number = {4},
pages = {471-481},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$},
url = {http://eudml.org/doc/298278},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Pérez-Hernández, Julio
AU - Pineda-Ruelas, Mario
TI - Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 4
SP - 471
EP - 481
AB - 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.
LA - eng
KW - ramification; cyclic quartic field; discriminant; index
UR - http://eudml.org/doc/298278
ER -

References

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