quasi algebraically closed field

In this paper,we discuss the classification of 3-dimensionally commutative algebras on algebraically closed field.

研究了代数闭域上三维交换代数的分类。

A theorem of integral divisibility for multivariate polynomial ring C[x 1,x 2,…,x n] on complex number field is given in [1], this paper extends the theorem to the case of k[x 1,x 2,…,x n] , where k is any algebraically closed field.

[1 ]给出复数域C上多元多项式环 C[x1 ,x2 ,… ,xn]的一类整除性定理 ,本文把它推广为任意代数闭域 k上多元多项式环 k[x1 ,x2 ,… ,xn]的情形 。

The two theorems are proved that any ring can be extended into an algebraically closed ring and that the quaternionic skew field over a real closed field is algebraically closed.

证明了任一环有代数封闭的扩张环,且实封闭域上的四元数体是代数封闭的,给出了代数封闭环的若干性质。