On Max-projective,PFP-module And H-finitely Generated Module

The paper uses mainly several kinds of special modules to probe into the properties of some rings. In chapter one, we provide some basic known definitions and important conclusions of projective modules, IF rings and semi-simple rings, and so on, which are needed in the paper. Due to the inspiration of maximal injective module by professor Wang Ming-yi, in chapter two, we introduce the conception of max-projective modules, discuss its properties, applications: the primitive relations between rings and endomorphism rings, an equivalence that is surrounding strongly V.N. rings. We apply individually the max-protectivity of finitely presented modules to give the relations between SF rings and V.N. rings if the rings are commutative or non-commutative. In chapter three, we popularize the strongly finitely presented modules to PFP-modules, give the relations between PFP-modules and Von Neumann rings, semi-simple rings. In chapter four, we discuss semi-simple rings, IF rings, V.N. rings and semi-perfect rings by using the H-finitely generated module, which is defined by Cobly in [2]. Meanwhile, we give equivalence between H-finitely presented modules and finitely presented modules in some condition.