模具有CS性质的环  

Rings Whose Modules Have CS Properties

作　　者：金慧萍[1] 

机构地区：[1]义乌工商职业技术学院,浙江义乌322000

出　　处：《西南师范大学学报（自然科学版）》2006年第6期4-6,共3页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：给出了模具有CS性质的环成为QF环、自内射环和连续环的一个充分条件:定理设R是左Kasch环,对于任意集A,若(R(A)是CS右R模,则R是QF环;(R(2)是CS右R模,则R是右自内射环;(R是CS右R模,则R是右连续环;如果每个CS右R模是X1ΣCS模,那么环R具有有限长度.This paper discussed rings whose modules have CS properties,the situation when which becomes a QF ring,self injective ring and continuous ring.The main results are the following:Let R be a left Kasch ring,if for any a set A,R^((A))(R^((2)),R) is right CS module,then R is QF(right self-injective,right continuous)ring.If every CS right R-module is X_1-Σ-CS module,then ring R have finite length.

关 键 词：CS模 右连续环 右自内射环 QF环 

分 类 号：O153.3[理学—数学]