Abstract: Let R be a commutative ring with identity, C be a semidualizing R-module and x be an exact zerodivisor over R. We considered the G_C-homological dimensions of modules under exact zerodivisors, and proved that if M was G_C-projective (injective, flat) R-module, then M/(xM) was G_C/(xC)-projective (injective, flat) R/(xR)-module. And the similar conclusions could be obtained for D_C-projective (injective) R-modules.

Key words: exact zerodivisor, G_C-projective (injective, , flat) module, G_C-projective (injective, flat) dimension