满足右零化子特殊升链条件的环

Rings Satisfying a Special Ascending Chain Condition for Right Annihilators

中文关键词:  右零化子特殊升链条件  右完备环  完全素理想

英文关键词:ascending chain condition for right annihilators  right perfect ring  completely prime ideal.

中文摘要:

      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．

英文摘要:

      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.