NON-MONOGENITY OF CERTAIN OCTIC NUMBER FIELDS DEFINED BY TRINOMIALS

被引：2

作者：

JAKHAR, A. N. U. J. ^{[1
]}

KAUR, S. U. M. A. N. D. E. E. P. ^{[2
]}

KUMAR, S. U. R. E. N. D. E. R. ^{[1
]}

机构：

[1] Indian Inst Technol IIT Bhilai, Dept Math, GEC Campus, Raipur 492015, Madhya Pradesh, India

[2] Panjab Univ Chandigarh, Dept Math, Chandigarh 160014, India

来源：

COLLOQUIUM MATHEMATICUM | 2023年 / 171卷 / 01期

关键词：

monogenity; theorem of Ore; prime ideal factorization; INTEGRAL BASES; INDEX;

D O I：

10.4064/cm8799-3-2022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K = Q (theta) be an algebraic number field with theta a root of an irreducible polynomial f (x) = x(8) + ax(m) + b is an element of Z[x] and 1 <= m <= 7. We study the monogenity of K. Precisely, we give some explicit conditions on a, b for which Kappa is non-monogenic. As an application of our results, we provide some classes of algebraic number fields which are non-monogenic. Finally, we illustrate our results through examples.

引用

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页码：145 / 152

页数：8

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