伪内射模与特殊环  

Pseudo-injective Modules and Special Rings

作　　者：班秀和[1] 韦儒和[1] 

机构地区：[1]广西师范学院数学与计算机科学系,广西南宁530001

出　　处：《阜阳师范学院学报（自然科学版）》2008年第2期12-14,共3页Journal of Fuyang Normal University(Natural Science)

基　　金：广西科学基金(0575052;0640070;桂科计字[2008]32号)

摘　　要：研究了伪内射模的性质,用伪内射模刻画了半单环,Noether、V-环,半Artin环和半局部环,得到的主要结果为:(1)伪内射模的完全不变子模是伪内射模;(2)R是半单环当且仅当伪内射模与半单模一致当且仅当半本原模是伪内射模,且本质基座的模是伪内射模当且仅当基座为0的模是伪内射模,伪内射模的直和伪内射;(3)R半Artin环当且仅当基座为0的模伪内射;(4)R是半局部环当且仅当R为左良好环且半本原模是伪内射模.In this paper,two properties of pseudo-injective modules are obtained. And semi-simple rings, Noetherian,V --rings, semi--Artinian rings, semi-local rings are characterized by pseudo-injective modules. The main results as follows ： （1） The fully invariant submodules of a pseudo-injective module are pseudo-injective; （2） R is a semi-simple ring iff pseudoinjective modules are coincident with semi-simple modules iff every semi-primitive module is pseudo-injective ,and every module that its socle is essential in it is pseudo-injective iff every module with zero socle is pseudo-injective.and the direct sum of pseudo-injective modules is pseudo-injective ; （3） R is a semi-Artinian ring iff every module with zero socle is pseudo-injective ;（4） R is a semi-local ring iff R is a left good ring,and semi-primitive modules are pseudo-injective modules.

关 键 词：伪内射模 半单环 NOETHER V-环 半Artin环 半局部环 

分 类 号：O153.3[理学—数学]