关于F-覆盖的存在性  

Note on the existence of F-covers

作　　者：宋贤梅[1] 

机构地区：[1]安徽师范大学数学系,安徽芜湖241000

出　　处：《山东大学学报（理学版）》2012年第10期4-6,13,共4页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10571026);安徽省教育厅重点研究项目(KJ2010A126);安徽师范大学专项基金(2008xzx10)

摘　　要：定义了一种模类-广义遗传预挠类F,即右R-模类F在纯子模,正向极限,纯满像下封闭。证明了若广义遗传预挠类F在扩张下封闭且R∈F,则每一个右R-模有F-覆盖。同时,还得到了当F是广义遗传预挠类时,每一个右R-模有F-预包络当且仅当F在直积下封闭。A generalized hereditary pretorsion class fare defined, that is the class of right R-module .f is closed under pure submodule, direct limits, and pure homomorphism image. It is shown that if fis a generalized hereditary pretor- sion class closed under extension and R ∈ f, then every fight R-module has an f--cover. And it is proved that if fis a generalized hereditary pretorsion class, then every fight R-module has an f-preenvelope if and only if fis closed under products.

关 键 词：f-覆盖 f-预覆盖 f-预包络 

分 类 号：O153.3[理学—数学]