We establish the equality between that the global dimension of an abelian category with enough projectives or injectives and the nilpotnece index of the ghost ideal in the category of complexes of this category. With this result, we provide a new approach to proof Hovey-Lockridge Theorem which states that if R is a left coherent ring, then the weakly global dimension of R is no more than n if and only if the (n + 1)-fold generating hypothesis holds for R.