拟代数闭域,quasi algebraically closed field

1)quasi algebraically closed field
拟代数闭域

2)algebraically closed field
代数闭域
1.
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。


2.
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 。



3)algebraic closed field
代数封闭域

4)algebraic closure of a field
域的代数闭包

5)algebraically closed
代数封闭
1.
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。



6)Weakly closed algebra
弱闭代数


补充资料：代数闭域


代数闭域
algebraically closed field

代数闭域【aigeb面回lyd姗d云eld“别.‘钾坪长。.3洲-幻乃7T此助月e] 域k.其l二的任何非零次多项式在丸中至少有个根.事实上，由此可推出一个代数闭域k上的任何。次多项式在k中恰有n个根，也即多项式环k【习中任不可约多项式都是一次的.域人是代数闭的，当且仅当它没有真的代数扩张(见域的扩张(extens，on of a field))·任何域k都有唯一的(仅差一同构)代数闭的代数.扩张;称之为k的华攀甲粤(al罗bra，e dosure)，通常用k表示.包含人的任何代数闭域都包含一个与万同构的子域. 复数域是实数域的代数闭包.这就是代数学基本定理(algebra，fundamental重heorem of).

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拟代数闭域,quasi algebraically closed field