Π-凝聚环的推广  

A Generalization of Π-coherent Rings

作　　者：余柏林[1] 汪明义[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2005年第3期278-281,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省教育厅重点科研基金;四川省青年基金资助项目

摘　　要：首先给出了AF 环的概念并列举了AF 环的一些性质与特征,证明了在AF 环上,IF 环与自FP 内射环是等价的,最后讨论了AF 环在对偶理论中的重要性.特别地,证明了若环R是一个自FP 内射的右AF 环,则R是QF环当且仅当R是一个左完全环.A ring R is said to be a right AF-ring if the right annihilator of every left ideal is finitely generated. In this paper, some equivalent characterizations and properties of AF-rings are listed. We prove that if R is left self P-injective and right AF-ring, then R is a right coherent ring. As a consequence, we prove that if R is an AF-ring, then R is an IF-ring if and only if R is self FP-injective. Finally, we consider AF-rings and their significance for the duality theory. In particular, it is proved that R is a QF ring if and only if R is left perfect ring and R is self FP-injective, under the condition that R is a right AF-ring.

关 键 词：Ⅱ-凝聚环 凝聚环 自FP-内射环 QF环 IF-环 完全环 

分 类 号：O153.3[理学—数学]