CLOSED AND PRIME IDEALS IN PARTIAL SKEW GROUP RINGS OF ABELIAN GROUPS

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 a is such a partial action and (T, beta) its globalization, then there exists a one-to-one correspondence between closed (respectively, R-disjoint prime) ideals of R star(alpha) G and closed (respectively, T-disjoint prime) ideals of T star(beta) G. We also prove that there exists a one-to-one correspondence between closed (respectively, R-disjoint prime) ideals of R star(alpha) G and closed (respectively, Q-disjoint prime) ideals of Q star(alpha) G, where Q is the left alpha-quotient ring of R. Finally, we use these results to study strongly prime ideals and nonsingular prime ideals of R star(alpha) G.