φ-平坦余挠理论

On φ -flat Cotorsion Theory

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.