强泛G-投射模,强泛G-内射模和强泛G-平坦模

Strongly Universal G-Projective,Injective and Flat Modules

【目的】完善相对同调理论中对强泛G-投射模、强泛G-内射模和强泛G-平坦模的研究。【方法】利用同调方法讨论了许多相关性质,举例给出了一个模是强泛G-投射模但不是强G-投射模。【结果】给出了强泛G-投射模(或强泛G-平坦模)是强G-投射模(或强G-平坦模)的充分条件,利用强泛G-投射模、强泛G-内射模和强泛G-平坦模的概念,刻画了强G-半单环、强G-Von Neumann正则环和强G-遗传环。【结论】补充了已有文献关于强泛G-投射模、强泛G-内射模和强泛G-平坦模性质的研究。

[Purposes]To complete the research of strongly universal G-projective modules,injective andflat modules in relative homology theory. [Methods] Many related properties are discussed by homology method. An example is given to show that a module is a strongly universal G-projective module,but not a SG-projective module. [Findings]A sufficient condition is giving to show that strong universal G-projective module（ or strong universal G-flat mode） is SG-projective（ or SG-flat）,the SG-semisimple ring,SG-Von Neumann regular ring and SG-hereditary ring are characterizedare characterized in terms of strongly universal G-projective,injective and flat modules. [Conclusions]The study of strongly universal G-projective modules,injective modules and flat modules is supplemented in existing papers.