Closed and prime ideals in partial skew group rings of abelian groups

摘要

In this paper we study partial actions of abelian groups on a ring R having an enveloping action. Among other results we prove that if α is such a partial action and (T, β) its globalization, then there exists a one-to-one correspondence between closed (respectively, R-disjoint prime) ideals of R *_α G and closed (respectively, T-disjoint prime) ideals of T *_β G. We also prove that there exists a one-to-one correspondence between closed (respectively, R-disjoint prime) ideals of R *_α G and closed (respectively, Q-disjoint prime) ideals of Q*_α G, where Q is the left α-quotient ring of R. Finally, we use these results to study strongly prime ideals and nonsingular prime ideals of R *_α G.