零可换环的一些性质  

SOME PROPERTIES OF ZERO COMMUTATIVE RINGS

作　　者：肖光世[1] 佟文廷[1] 

机构地区：[1]南京大学数学系

出　　处：《数学年刊（A辑）》2005年第2期251-256,共6页Chinese Annals of Mathematics

摘　　要：本文刻画了零可换环的一些性质,同时将交换环上的一些结果推广到零可换环上.对于零可换环R 证明了: (1)R是强正则环当且仅当R中每个为零化子的本质左理想是左GP.内射模或R中存在一个极大左理想K,使得K中每个元索的零化子是左GP-内射模; (2)R是GPP-环当且仅当R是拟π-正则的GPF-环.This paper investigates some properties of zero commutative rings and extend some results from commutative rings to zero commutative rings. If R is a zero commutative ring, the authors obtain that (1) R is strongly regular if and only if every essential left ideal of R which is an annihilator is left GP-injective or R contains a maximal left ideal K such that the annihilator of every element of K is left GP-injective; (2) R is a GPP-ring if and only if it is a quasi π-regular ring and GPF-ring.

关 键 词：GPP-环 GPF-环 广义π-正则环 零可换环 零插入环 

分 类 号：O153.3[理学—数学]