Abstract
The aim of this paper is to determine the monogenity of imaginary,
and real biquadratic fields K over the field Q of rational numbers and the relative
monogenity of K over its quadratic subfield k. To characterize such phenomena it
is necessary to determine an integral basis of the field K and to evaluate the relative norm of the different d(ξ) with respect to K/k of an integer ξ in K. Here
d(ξ) is defined by Q
ρ∈G\{ι}
(ξ − ξ
ρ
), where ξ − ξ
ρ
denotes the partial different
of an integer ξ in K, and G and ι denote the Galois group of K/Q and the identity
embedding of K, respectively. For the succinct proof of non-monogenity, we consider a single linear Diophantine equation consisted of the partial differents with
unit coefficients.
Mamoona Sultan, Yoshifumi Kohno, Toru Nakahara. (2015) Monogenity of Biquadratic Fields Related to Dedekind-Hasse’s Problem, Punjab University Journal of Mathematics, Volume 47, Issue 2.
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