1) right annihilator
右零化子
2) right divisor of zero
右零因子
3) ascending chain condition for right annihilators
右零化子特殊升链条件
1.
In this paper some properties of the rings satisfying a special ascending chain condition for right annihilators, and some relations to left, ringt perfect rings and QF righs are discussed; As an application of Goldie theorem, a condition is given for a prime ideal is a completely prime ideal in this class of rings.
本文讨论了满足右零化子特殊升链条件的环的性质以及与左、右完备环，ＱＦ－环的关系；给出了满足右零化子特殊升链条件的环中素理想是完全素理想的条件，从而给出了Ｇｏｌｄｉｅ定理的一个应用。
4) the descending chain condition for special right annihilators
特殊右零化子降链条件
5) left(right) zero divisor
左(右)零因子
1.
This parer proved that for the ring R with n left(right) zero divisors, if |R|=n 22 ,then n=2 s+1 (n∈N),|R|=2 2s+1 and the character of R could only be 2,4 or 8;and if R is the commutative ring whose character is 2, then R could only be the 8 element ring with 4 zero divisors.
证明了具有ｎ（＞２）个左（右）零因子的环Ｒ，当｜Ｒ｜＝ｎ２２时，必有ｎ＝２ｓ＋１（ｓ∈Ｎ），｜Ｒ｜＝２２ｓ＋１，且Ｒ的特征是２，４或８。
6) annihilating right ideal
零化右理想
补充资料：零化子
零化子
annMator
零化子【叨n谢面叙盯;aI.卿几.1.pl，R中集合X的左 R中所有使夕X=0的元素y的集合3，(X).这里的R是环或具有零的半群(或一般地，广群).用类似的方法，R中集合的右零化子(right annihihtor)定义为集合 旅(幻=(:。R:Xz=0}.集合 3(X)=3，(X)门3。(X)是X的双边零化子(。刀。一sided annihilator).在结合环(或半群)R中任意集合X的左零化子是左理想，如X是R的左理想，则3，(X)是R的双边理想;在非结合的情形，这些结论通常不成立.
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