摘要
利用Galois理论,研究了4次根式扩张的一些性质.利用这些性质,给出了域扩张是4次根式扩张的一些等价条件,证明了域扩张是4次根式扩张当且仅当域扩张是4次Galois扩张且Galois群是4阶循环群.
Some properties of quartic radical extensions are discussed by using Galois theory.Furthermore,some sufficient and necessary conditions for field extensions to be quartic radical extensions are obtained through these properties.Finally,it is proved that field extensions are quartic radical extensions,if and only if field extensions are quartic Galois extensions and Galois group is 4-order cyclic.
作者
张文华
姜小龙
ZHANG Wen-hua;JIANG Xiao-long(Department of Mathematics,Jining University,Qufu 273155,China;Department of Mathematics,Sun Yat-sen University,Guangzhou510275,China)
出处
《数学的实践与认识》
北大核心
2019年第8期188-192,共5页
Mathematics in Practice and Theory
基金
国家自然科学基金(11171356)
山东省自然科学基金(ZR2017PA001)
济宁学院博士科研启动资金专项(2017BSZX01)
