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

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 th...

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Autores principales:	Julio Pérez-Hernández, Mario Pineda-Ruelas
Formato:	article
Lenguaje:	EN
Publicado:	Institute of Mathematics of the Czech Academy of Science 2021
Materias:	ramification cyclic quartic field discriminant index Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b53e413f273d4bfdbc6e3402c62aeb85
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spelling	oai:doaj.org-article:b53e413f273d4bfdbc6e3402c62aeb852021-11-08T09:59:12ZRamification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$0862-79592464-713610.21136/MB.2021.0131-19https://doaj.org/article/b53e413f273d4bfdbc6e3402c62aeb852021-12-01T00:00:00Zhttp://mb.math.cas.cz/full/146/4/mb146_4_7.pdfhttps://doaj.org/toc/0862-7959https://doaj.org/toc/2464-7136If $K$ 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.Julio Pérez-HernándezMario Pineda-RuelasInstitute of Mathematics of the Czech Academy of Sciencearticle ramification cyclic quartic field discriminant indexMathematicsQA1-939ENMathematica Bohemica, Vol 146, Iss 4, Pp 471-481 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	ramification cyclic quartic field discriminant index Mathematics QA1-939
spellingShingle	ramification cyclic quartic field discriminant index Mathematics QA1-939 Julio Pérez-Hernández Mario Pineda-Ruelas Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
description	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.
format	article
author	Julio Pérez-Hernández Mario Pineda-Ruelas
author_facet	Julio Pérez-Hernández Mario Pineda-Ruelas
author_sort	Julio Pérez-Hernández
title	Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
title_short	Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
title_full	Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
title_fullStr	Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
title_full_unstemmed	Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$
title_sort	ramification in quartic cyclic number fields $k$ generated by $x^4+px^2+p$
publisher	Institute of Mathematics of the Czech Academy of Science
publishDate	2021
url	https://doaj.org/article/b53e413f273d4bfdbc6e3402c62aeb85
work_keys_str_mv	AT julioperezhernandez ramificationinquarticcyclicnumberfieldskgeneratedbyx4px2p AT mariopinedaruelas ramificationinquarticcyclicnumberfieldskgeneratedbyx4px2p
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Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$

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