CP-injective Modules And CP-flat Modules

In this paper, CP-injective modules, CP-flat modules and CP-projective mod-ules are investigated. First of all, we introduce the notion of CP-injective moduleand CP-flat module, study the existence of CP-injective cover (CP-flat cover) andCP-injective preenvelope (CP-flat preenvelope) of a module. Secondly, we introducethe CP-injective dimension and CP-flat dimension of a module, then we give someequivalent characterizations of these dimensions over left strongly P-coherent ring.Finally, we study the CP-injective modules, CP-flat modules under the excellent ex-tensions of the rings, by means of the CP-injective module introduced and studiedthe CP-projective module and its dimension.