Turkish Journal of Mathematics
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 $\mathbb{Q}(\sqrt{-a\varepsilon_p\sqrt{p}})$.
DOI
10.3906/mat-2101-120
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
