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.
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页码：145 / 152
页数：8
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