GV-平坦模  

GV-flat modules

作　　者：张晓磊 ZHANG Xiao-lei(School of Mathematics and Statistics,Shandong University of Technology,Zibo 255000,Shandong,China)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255000

出　　处：《西北师范大学学报（自然科学版）》2023年第5期29-34,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12061001)。

摘　　要：研究GV-平坦模及其盖包理论.利用GV-平坦模给出了DW-环和von Neumann正则环新的等价刻画;证明了任意模都有GV-平坦盖;环R是GV-凝聚环当且仅当任意R-模都有GV-平坦预包.通过具体例子区分了GV-平坦模和w-平坦模、GV-凝聚环和w-凝聚环.The GV-flat modules and its covering properties are discussed.The DW-rings and von Neuamnn regular rings are characterized by utilizing GV-flat modules.It is proved that any R-module has a GV-flat cover,and a ring R is GV-coherent if and only if any R-module has a GV-flat preenvelope.Some concrete examples are given to distinguish GV-flat modules and w-flat modules,GV-coherent rings and w-coherent rings.

关 键 词：GV-平坦模 GV-凝聚环 平坦盖 平坦预包 

分 类 号：O154.2[理学—数学]