The Generalization Of P-flat Modules And P-injective Modules

This paper mainly study n-P-flat modules, n-P-injective modules and n-P-coherent rings.Firstly we discuss the property of n-P-flat modules and n-P-injective modules,and use them to characterize n-P F rings, n-P P rings and n-regular rings. Secondly,we introduce n-P-coherent rings, and prove that any left R-module has an epic n-PI-cover equal to any right R-module has a monic n-PF-preenvelope under thecondition of n-P-coherent rings.