基于拓扑方法的代数基本定理的证明

A Proof on Fundamental Theorem of Algebra Based on Topological Method

代数基本定理在代数学乃至整个数学研究起着最基础的重要作用。因而,对代数基本定理的进一步探讨将是十分有趣的。在复系数情形下,Frode Terkelsen给出了一个既初等而又相当简洁的证明,周玛莉用映射的观点证明了代数基本定理,但几乎所有证明方法都没有离开复数域的解析性质。现在已有研究成果的基础上,给出代数基本定理的拓扑思想方法的既直观又初等的证明。

Fundamental theorem of algebra is playing most important basic role in the algebra,even in the entire mathematics studies.Thus,further exploration of the theorem will be very interesting.Frode Terkelsen gives an elementary and brief prove with the complex eertification,Zhou Mali shows fundamental theorem of algebra with the mapping point.But almost all of the methods did not leave the complex domain＇s analysis nature.The visible and elementary proof will be given to the algebraic method of fundamental theorem of algebra.