Some Kinds Of Generalized Injectivity Of S-acts

In this thesis,we mainly discuss several kinds of generalized injectivity of S-acts and some recursive relationships between them.Firstly,we study the characterizations of two special types of injective acts,which are called P-principally weakly injective acts and CP-injective acts.We give the properties of the two kinds of injective acts.Using the two new properties,the characterizations of some new classes of monoids are obtained.Meanwhile,we study the differences and relations between Pprincipally weakly injective acts and principally weakly injective acts,CP-injective acts and CC-injective acts.Secondly,we define LCINC-injective acts and LCCinjective acts and equivalent characterizations of them are studied.We also discuss the relationship between the extension forms of injective acts.In addition,we give the homological classification problems of monoids by LCINC-injective acts and LCC-injective acts.Finally,the recursive relationships among the LCINC-injective acts,the LCC-injective acts and the existing injective acts are summarized.