左JGP-V′-环的若干性质  

Some Properties of Left JGP-V′-Rings

作　　者：胡高明 吴俊 HU Gaoming;WU Jun(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241003,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《南通大学学报（自然科学版）》2018年第2期55-58,共4页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11401009)

摘　　要：若每个单奇异左R-模都是JGP-内射模,则称环R为JGP-V′-环.文章主要研究了JGP-V′-环的非奇异性和半本原性,证明了如下结果:1)若R是左JGP-V′-环,则Z(RR)∩J(R)=0;2)若R是左拟duo-环、左JGP-V′-环,则R是左非奇异环;3)若R是左拟duo-环、左JGP-V′-环,则R是半本原环.A ring R is called left JGP-V′-ring, if every simple singular left R-module is JGP-injective. In this paper,the non-singularity and the semiprimity of left JGP-V′-rings were studied, and results revealed that ： 1） If R is a left JGP-V′-ring, then Z（RR）∩J（R） = 0;2）If R is a left quasi duo ring and JGP-V′-ring, then R is left non-singular;3）If R is a left duo ring and JGP-V′-ring, then R is semiprimitive.

关 键 词：JGP-内射模 JGP-V′-环 非奇异环 半本原环 

分 类 号：O153.3[理学—数学]