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, M. A, & EDDIN, M. M (2021). On Hilbert genus fields of imaginary cyclic quartic fields. Turkish Journal of Mathematics 45 (4): 1689-1704. https://doi.org/10.3906/mat-2101-120
