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。
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。