φ-平坦余挠理论  

On φ -flat Cotorsion Theory

作　　者：张晓磊 赵伟 王芳贵 ZHANG Xiaolei;ZHAO Wei;WANG Fanggui(School of Mathematical Sciences,Sichuan Normal University,Chengdu Sichuan 610068,China;School of Mathematics and Computer Science,Aba Teachers University,Aba Sichuan 623002,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610068 [2]阿坝师范学院数学与计算机科学学院,四川阿坝623002

出　　处：《广西师范大学学报（自然科学版）》2021年第2期119-124,共6页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11671283)。

摘　　要：引进并研究φ-平坦余挠理论,证明了该余挠理论是完全余挠理论。设R是φ-环,则φ-平坦余挠理论与经典平坦余挠理论相等当且仅当R是整环。作为应用,给出了非诣零凝聚环和φ-VN正则环的新刻画和φ-平坦模的包类性质;证明了每个R-模都有一个满的φ-平坦包当且仅当R是非诣零凝聚环,并且φ-平坦模关于子模封闭。In this paper,theφ-flat cotorsion theory which is showed to be a perfect cotorsion theory is introduced and studied.Assume R is aφ-ring.It is proved that theφ-flat cotorsion theory coincides with the classical flat cotorsion theory if and only if R is a domain.As an application,new characterizations of Nonnil-coherent rings andφ-von Neumann rings are given.Finally,the envelope property ofφ-flat modules is investigated and showing that every R-module has a surjective(pre)envelope if and only if R is a Nonnil-coherent ring and allφ-flat R-modules are closed under submodules.

关 键 词：余挠理论 盖类 包类 φ-平坦模 φ-余挠模 

分 类 号：O154.2[理学—数学]