C2 Rings And Strongly CF Rings

C1 and C2 rings were defined by Y.Utumi in 1965. He called a ring continuous if it is both C1 and C2. Continuous rings are generalizations of injective rings. Nicholson, Yousif, Chen, Ding and Zhou have studied C2 rings since 1999. Based on their researches, more sdudies on C2 rings are made in this thesis. Strongly right CF rings are introduced and studied in this paper.In the second chapter, firstly we study extentions of n-C2 rings and generalize a recent result of Chen, Ding and Zhou. Secondly we study GC2 ring, a special case of n-C2 rings and give conditions under which right GC2 rings are right artinian, injective and directly finite. We also study extentions of C2 rings and independly answer a question of Nicholson and Yousif in the negative and generalize a result of Chen, Ding and Zhou.In the third chapter, firstly we study weakly continuous and generalized continuous rings with certain chain conditions and give new characterizations of QF rings. They are generalizations of results of Chen, Li, Shen, Zhou, Nicholson and Yousif. At last, we study strongly right CF rings and give conditions under which strongly right CF rings are right artinian and QF. A new characterization of right special rings is obtained.