域扩张是单根式塔的充分必要条件

J4 ›› 2013, Vol. 48 ›› Issue (2): 32-35.

域扩张是单根式塔的充分必要条件

张文华¹,姜小龙²,王珍¹

1.济宁学院数学系, 山东曲阜 273155; 2.中山大学数学系, 广东广州 510275

收稿日期:2012-05-30 出版日期:2013-02-20 发布日期:2013-03-04
作者简介:张文华(1973- ),男,硕士,讲师,研究方向为代数与编码. Email: ytzwh@163.com
基金资助:
国家自然科学基金资助项目(10971233);山东省优秀中青年科学家科研奖励基金资助项目(BS2010DX004);济宁学院青年科研基金资助项目(2010QNKY08)

Sufficient and necessary conditions for field extensions to be simple radical towers

ZHANG Wen-hua1, JIANG Xiao-long2, WANG Zhen1

1. Department of Mathematics, Jining University, Qufu 273155, Shandong, China;
2. Department of Mathematics, Sun Yatsen University, Guangzhou 510275, Guangdong, China

Received:2012-05-30 Online:2013-02-20 Published:2013-03-04

摘要/Abstract

摘要：

设K是域F的扩张,利用Galois理论,给出了K是F的单根式塔的一些充分必要条件,并证明了在某些条件下, 单根式塔与Galois扩张是等价的。

关键词: 域扩张;单根式塔;根式扩张;本原单位根

Abstract:

Let F be a field and K be an extension field of F. Some sufficient and necessary conditions such that K is a simple radical tower of F are given by using primitive root of unity and Galois theory. Moreover, it is proved that under certain conditions K is a simple radical tower of F if and only if K is Galois over F.

Key words: field extension; simple radical tower; radical extension; primitive root of unity

张文华1,姜小龙2,王珍1. 域扩张是单根式塔的充分必要条件[J]. J4, 2013, 48(2): 32-35.

ZHANG Wen-hua1, JIANG Xiao-long2, WANG Zhen1. Sufficient and necessary conditions for field extensions to be simple radical towers[J]. J4, 2013, 48(2): 32-35.

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