Affiliation:
1. Faculty of Sciences Dhar El Mahraz, Sidi Mohamed ben Abdellah University , P.O. Box 1796 Atlas-Fes , MOROCCO , lhouelfadil2@gmail.com
Abstract
ABSTRACT
Let K be a number field generated by a root θ of a monic irreducible trinomial
F
(
x
)
=
x
n
+
a
x
m
+
b
∈
ℤ
[
x
]
. In this paper, we study the problem of monogenity of K. More precisely, we provide some explicit conditions on a, b, n, and m for which K is not monogenic. As applications, we show that there are infinite families of non-monogenic number fields defined by trinomials of degree n = 2
r
· 3
k
with r and k two positive integers. We also give infinite families of non-monogenic sextic number fields defined by trinomials. Some illustrating examples are giving at the end of this paper.
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