兰州理工大学学报

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (4): 146-150.

• 数理科学 • 上一篇    下一篇

GV-Noether环及其弱GV-内射模

张晓磊*, 齐薇   

  1. 山东理工大学 数学与统计学院, 山东 淄博 255000
  • 收稿日期:2022-05-04 出版日期:2023-08-28 发布日期:2023-08-29
  • 通讯作者: 张晓磊(1986-),男,山东青岛人,博士,讲师. Email:zxlrghj@163.com
  • 基金资助:
    国家自然科学基金(12061001,12201361)

GV-Noetherian rings and their weak GV-injective modules

ZHANG Xiao-lei, QI Wei   

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
  • Received:2022-05-04 Online:2023-08-28 Published:2023-08-29

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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.

关键词: GV-Noether环, 弱GV-内射模, GV-内射模, DW-环, VN正则环

Abstract: 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.

Key words: GV-Noetherian ring, weak GV-injective module, GV-injective module, DW-ring, von Neumann regular ring

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