| This thesis consists of two chapters.In Chapter 1, the Factor Theorem are generalized and an equivalent condi-tion for exact sequence is obtaided: a sequence is exact iff there exists a commu-tative diagram which the "diagonal" sequences are all exact.In Chapter 2, we study equivalent conditions for projective S-acts and in-jective S-acts. In the central S-acts category, some equivalent conditions for acogenerator and a genenrator are given. By using the natural isomorphisms offunctors, we obtain some characterizations for a flat S-acts. Some relations amonginjective cogenerator, projective, injective and generator are also obtained. |
