This thesis is devoted to the study of the homological dimension, homological homogeneity and injective homogeneity of the skew group rings, crossed products, group graded rings and the Ore extensions; and to the study of the Auslander-Gorenstein, the Auslander-regular and the Macaulay properties of the injectively homogeneous rings and the homologically homogeneous rings. In chapter 2, we study the global dimension of skew group rings, crossed products and group graded rings. In chapter 3 we first study the injective homogeneity of crossed products, then use the smash products machinery to extend our results to strongly group graded rings. In chapter 4, We come to study the Auslander-Gorenstein, the Auslander-regular and the Macaulay properties of injectively homogeneous and homologically homogeneous Noetherian rings which are integral over their centres.