关于域的扩张研究

Research on the Extension of Fields

域的扩张是域的一项重要的研究内容,根据已有的域,通过扩张的方法,可以构造新的域;代数扩张能将有理数域扩充为实数域,实数域添上虚数单位i可以扩充为复数域,而有限扩张和代数扩张又有着重要联系;在有限扩张与代数扩张的基本性质的基础上,进一步探讨了实数域扩充为复数域的过程.

Extension of fields is an important research content.Based on the existing fields,by the method of extension,new fields can be constructed.The understanding of number for people is the process of the extension of number fields.Algebraic extension can expand rational number field to real number field,real number field with the imaginary unit can be extended to complex field,and finite extension and algebraic extension have important connection. Based on the basic properties of the finite extension and algebraic extension,this paper researches the process of the extension of the real number field to the complex field.