Gorenstein Homological Dimensions Of Mod-Ules Under Exact Zero-divisors And Global Ding Projective Dimensions Of Rings

Let C be a semi-dualizing module and x is an exact,zero-divisor on R.In this pa-per,we mainly investigate Ding homological dimensions of modules and rings.First-ly,We discuss Ding projective dimensions and Gorenstein homological dimensions under exact zero-divisor;Secondly,Ding projective dimensions and Gorenstein ho-mological dimensions with respect to a semi-dualizing module C are discussed under exact zero-divisor;Thirdly,we prove that the global Ding projective dimensions of ring R is equal to the supremum of the set of Ding projective dimensions of all cyclic R-modules,furthermore,a good equivalent characterization is given for Ding global dimensions of Ding-Chen ring.