Article Title

On Hilbert genus fields of imaginary cyclic quartic fields

Authors

MOULAY AHMED HAJJAMI
MOHAMED MAHMOUD CHEMS EDDIN

DOI

10.3906/mat-2101-120

Abstract

Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. Let $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ be a positive square-free integer. The main aim of this paper is to determine explicitly the Hilbert genus field of the imaginary cyclic quartic fields of the form $\mathbb{Q}(\sqrt{-a\varepsilon_p\sqrt{p}})$.

Keywords

Imaginary cyclic quartic fields, unramified extensions, Hilbert genus fields

First Page

1689

Last Page

1704

Recommended Citation

HAJJAMI, MOULAY AHMED and EDDIN, MOHAMED MAHMOUD CHEMS (2021) "On Hilbert genus fields of imaginary cyclic quartic fields," Turkish Journal of Mathematics: Vol. 45: No. 4, Article 17. https://doi.org/10.3906/mat-2101-120
Available at: https://journals.tubitak.gov.tr/math/vol45/iss4/17