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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