About Simple-Projective Modules, Soc-Flat Modules, Soc-Pseudo Modules

This thesis is made up of three chapters:The first chapter defines simple-projective modules.Some equivalent conditions and some characterizations of simple-projective modules are given;More over,we introduce the left SP-rings and prove that the left SP-rings are Morita invariant.Next,left V-rings are characterized by simple-projective modules;At last,we prove the Schanuel Lemma,which is in relation to simple-projec-tive modules.The second chapter defines soc-flat modules and strongly soc-flat mod-ules.Some equivalent conditions and some characterizations of soc-flat modules are given.More over,we use the two modules to character right perfect rings,FS rings and soc-regular rings;Next,we introduce the co-torsion theory of modules,and prove that soc-regular rings and soc-IF are equivalent under special conditions by the hereditary cotorsion theory;At last,we give the definitions of the soc-flat dimension of the right modules and the right soc-weak dimension of the rings,consider some properties about them and introduce the relation of the right soc-weak dimension and the FS rings.The third chapter give the definition of soc-pseudo injective modules. Some equivalent conditions and some characterizations of soc-pseudo in-jective modules are given.Next,we define the injective socle of modules and get some characterizations about it;At last,we have a discussion about the S-rings,and show that semisimple rings are S-rings.