GV-Noether环及其弱GV-内射模  

GV-Noetherian rings and their weak GV-injective modules

作　　者：张晓磊 齐薇 ZHANG Xiao-lei;QI Wei(School of Mathematics and Statistics,Shandong University of Technology,Zibo 255000,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：《兰州理工大学学报》2023年第4期146-150,共5页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(12061001,12201361)。

摘　　要：给出了GV-Noether环的Cartan-Eilenberg-Bass定理.引进了弱GV-内射模并刻画了DW-环和VN正则环.特别地,证明了环R是VN正则环当且仅当任意弱GV-内射R-模是绝对纯R-模,当且仅当任意弱GV-内射R-模是余平坦R-模.给出了GV-Noether环的Megibben定理.通过提供一些例子区别Noether环,GV-Noether环和w-Noether环.The Cartan-Eilenberg-Bass Theorem for GV-Noetherian rings is given.The class of weak GV-injective modules is introduced to characterize DW-rings and von Neumann regular rings.In particular,it is proved that the ring is von Neumann regular if and only if any weak GV-injective module is an absolutely pure module,and if and only if any weak GV-injective module is coflat.Finally,the Megibben Theorem for GV-Noetherian rings is obtained.Meanwhile,some examples are provided to distinguish Noetherian rings,GV-Noetherian rings,and w-Noetherian rings.

关 键 词：GV-Noether环 弱GV-内射模 GV-内射模 DW-环 VN正则环 

分 类 号：O154.2[理学—数学]