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We study near-rings N with the property (∗) : xS = Sx for each x ∈ N and each n-subset S of N . By localizing (∗), we obtain center-like subsets, which we study for the case of rings. In response to a question of B.H. Neumann, we defined a Qn–ring to be a ring R with the property that xS = Sx for all x ∈ R and all n-subsets S of R. In [3] we investigated basic properties of Qn–rings and establi...