Let R be a ring and G a finite group of automorphisms of R such that GL-1ε R. In the first section, we study the homological and injective dimensions of RGwhen R is simple. In the second section, we suppose that R is a k-algebra and study c,the transfer of the Nullstellensatz property between R and RGIn the last section, we apply these results to envelopping atgebras of Lie algebras and Weyl algebras.