S-injective Module And S-injective Dimension

Through the introduction of the notion of S-injective module: let E be a leftR-module, if Ext_R~1(N,E) = 0 for any N∈S, we study some important propertiesabout generalized injective module. for example: the Baer rule of the generalizedinjective module, the existence of the generalized injective envelope, the gener-alized injective dimension of modules. This thesis is divided into two chapters.In chapter one, section one, we introduce modular variety: S-modular variety,complete modular variety, Baer modular variety. In chapter one, section two, weintroduce the notion of S-injective module, and illuminate the relationship amongS-injective module and injective module, FP-injective module, f-injective mod-ule and so on, then give some equivalent characterizations about it, and discusssome properties of it. In chapter one, section three, we introduce the notion of S-essential extension of module, and then define S-injective envelope on that basis,and we obtain a series of properties about S-injective envelope. In chapter one, section four, we introduce the notion of S-flat module, then give some equivalentcharacterizations about it, and discuss some properties of it. In chapter two, wedefine S-injective dimension, then give some properties and results, then studyS-flat dimension.