关于S-投射模  

On Singly Projective Modules

作　　者：张永亮[1] 丁南庆[2] 

机构地区：[1]安康学院数学与统计系,陕西安康725000 [2]南京大学数学系,江苏南京210093

出　　处：《四川师范大学学报（自然科学版）》2015年第6期846-850,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11171240);国家自然科学数学天元基金(11226057)

摘　　要：设R为任意的幺环.Azumaya将投射模的概念推广到S-投射模.文献(Zhu S L.J Algebra,1991,139:255-261.)讨论了在什么样的环上,平坦模是f-投射的.文献(Mao L X.Taiwan Residents J Math,2007(12):501-512.)给出了内射模都是S-投射的环.讨论S-投射模和其他模的关系,如投射模、平坦模、拟内射模、可除模、S-平坦模等,并证明了S-投射模关于直和的封闭性.Let R be a ring. Azumaya generalized the concept of projectivity of modules to single projectivity. The paper （Zhu S L. J Algebra,1991,139：255 -261. ） argued about rings over which every fiat module is finitely projective. And the paper （Mao L X. Taiwan Residents J Math,2007 （12） ：501 -512. ） gave a condition when every injective R-module is singly projective. This article shows some other relations between singly projective R-modules and other kinds of modules, such as quasi-injective R-modules, singly fiat R-mod- ules, finitely projective R-modules and divisible R-modules. And it is proved that singly projective modules are closed under direct sums.

关 键 词：S-投射模 平坦模 S-平坦模 

分 类 号：O153.3[理学—数学]