We study primality, hypercentrality, simplicity, and localization and the second layer condition in skew group rings and group-graded rings. We give necessary and sufficient conditions for the skew group ring of a torsion-free nilpotent group to be a simple ring, and if the coefficient ring is commutative, we give necessary and sufficient conditions for the skew group ring of an Abelian group to be simple. Our method involves showing certain group-graded rings are hypercentral. Our main results show that if $G$ is a polycyclic-by-finite group and $R$ is an Artinian ring or a commutative Noetherian ring, then a strongly $G$-graded ring with base ring $R$ satisfies the second layer condition. We discuss consequences of this for localization in such rings.
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