On The Discussion Of The Stability Of C-Gorenstein Categories And Homological Dimensions

In this paper, we mainly study the GC-flat dimensions of complexes and the stability of the Gorenstein homological modules with respect to a semidualizing module. Firstly, the stability of GC-injective(flat) modules and the corresponding complexes are proved. Then, GC-flat dimensions of modules are introduced, and equivalent descriptions of GC-flat dimensions less than n is given. Finally, we in-troduce GC-flat dimensions of complexes by hyper homological method, some nice functorial descriptions about GC-flat dimensions of complexes are given, generalize the existing conclusions.