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

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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, [Formula: see text]-disjoint prime) ideals of [Formula: see text], where [Formula: see text] 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.