Strong C - Gorenstein Flat Die

Let R be a ring with unit, a left R module M is called a Strong C Gorenstein flatmodule if it satisfies the following:(1)there exists a exact sequence ofPCmodules:â†'C RP1â†'C RP0â†'C RP0â†'C RP1â†'(2) M～=ker(C RP0â†'C RP1).(3)the functor H omR(,FC) is exact with (1).Firstly, in the third section, we get some main properties about Strong C Gorensteinflat module:(1)any Strong C Gorenstein flat module is a C Gorenstein flat module.(2)if R is an n Gorenstein ring, then R module M is a Strong C Gorenstein flatmodule if and only if M is a C Gorenstein projective module with a C projectiveresolution.Secondly, in the forth section, we denote the definition of Strong C Gorenstein flatdimension of a right R module M. And by applying the basic methods of homologicalalgebra, we get the corresponding conclusions relative to Strong C Gorenstein flat mod-ules as following: the R module exact sequence0â†'Kâ†'Lâ†'Mâ†'0, if any two ofSGfCdR(K), SGfCdR(L) and SGfCdR(M) are finite, so is the third. Moreover, we getthe relationships among SGfCdR(K), SGfCdR(L) and SGfCdR(M).