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.
Reference31 articles.
1. AHMAD, S.—NAKAHARA, T.—HAMEED, A: On certain pure sextic fields related to a problem of Hasse, Int. J. Alg. Comput. 26(3) (2016), 577–583.
2. BEN YAKKOU, H.—EL FADIL, L.: On monogenity of certain number fields defined by trinomials, Funct. Approx. Comment. Math. 67(2) (2022), 199–221.
3. CARLITZ, L.: A note on common index divisors, Proc. Amer. Math. Soc. 3 (1952), 688–692.
4. COHEN, H.: A Course in Computational Algebraic Number Theory. GTM 138, Springer-Verlag Berlin Heidelberg, 1993.
5. DEDEKIND, R.: Uber den Zusammenhang zwischen der Theorie der Ideale und der Theorie der hUheren Kongruenzen, Göttingen Abhandlungen 23 (1878), 1–23.
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献