Finiteness of relative Gorenstein homological dimensions.

Let be an abelian category and (,) a pair of classes of objects in . Inspired by Bouchiba's work on generalized Gorenstein projective modules, we give a new way of measuring (,) -Gorenstein projective dimension by defining a complete n - (,) resolution. Then we relate the relative global Gorenstein homological dimension to the invariants silp() and spli() under some conditions. Furthermore, we prove that, in the setting of a left and right coherent ring R , the supremum of Ding projective dimensions of all finitely presented (left or right) R -modules and the (left or right) Gorenstein weak global dimension are identical, generalizing a theorem of Ding, Li and Mao. [ABSTRACT FROM AUTHOR]