On Index Divisors and Monogenity of Certain Sextic Number Fields Defined by x6+ax5+b

被引：0
|
作者：
El Fadil, Lhoussain [1 ]
Kchit, Omar [1 ]
机构：
[1] Sidi Mohamed ben Abdellah Univ, Fac Sci Dhar El Mahraz, POB 1796, Atlas Fes, Morocco
来源：
VIETNAM JOURNAL OF MATHEMATICS | 2024年
关键词：
Theorem of Dedekind; Theorem of Ore; Prime ideal factorization; Newton polygon; Index of a number field; Power integral basis; Monogenic; POLYGONS;
D O I：
10.1007/s10013-023-00679-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main goal of this paper is to provide a complete answer to the Problem 22 of Narkiewicz (2004)} for any sextic number field K generated by a complex root alpha of a monic irreducible trinomial F(x)=x(6)+ax(5)+b is an element of Z[x]. Namely we calculate the index of the field K. In particular, if i(K)not equal 1, then K is not mongenic. Finally, we illustrate our results by some computational examples.
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页数：14
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