Partial Skew Group Rings Over Polycyclic by Finite Groups

Abstract

In this paper we consider a partial action α of a polycyclic by finite group G on a ring R. We prove that if R is right noetherian, then the partial skew group ring R ⋆ αG is also right noetherian. Extending the methods of Passman in Passman (Trans Am Math Soc 301:737–759, 1987), we obtain a description of the prime spectrum of R ⋆ αG. The results obtained are applied to get bounds for the Krull dimension and the classical Krull dimension of R ⋆ αG.