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We catalogue the primitive ideals of the Cuntz-Krieger algebra of arow-finite higher-rank graph with no sources. Each maximal tail in the vertexset has an abelian periodicity group of finite rank at most that of the graph;the primitive ideals in the Cuntz-Krieger algebra are indexed by pairsconsisting of a maximal tail and a character of its periodicity group. TheCuntz-Krieger algebra is primitive if and only if the whole vertex set is amaximal tail and the graph is aperiodic.

The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources