域扩张是单根式塔的充分必要条件 |
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引用本文: | 张文华,姜小龙,王珍.域扩张是单根式塔的充分必要条件[J].山东大学学报(理学版),2013,48(2):32-35. |
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作者姓名: | 张文华 姜小龙 王珍 |
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作者单位: | 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 |
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基金项目: | 国家自然科学基金资助项目,山东省优秀中青年科学家科研奖励基金资助项目,济宁学院青年科研基金资助项目 |
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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。
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关 键 词: | 域扩张 单根式塔 根式扩张 本原单位根 |
收稿时间: | 2012-05-30 |
Sufficient and necessary conditions for field extensions to be simple radical towers |
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Institution: | 1. Department of Mathematics, Jining University, Qufu 273155, Shandong, China;
2. Department of Mathematics, Sun Yat sen University, Guangzhou 510275, Guangdong, China |
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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. |
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Keywords: | field extension simple radical tower radical extension primitive root of unity |
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