This work gives a characterization of distributive pairs of nilrings and of arithmetic, nilpotent rings by means of a method analogous to that one developed by Stephenson for the discussion of distributively representable rings. The results are nearly the same as Suzuki's on distributive pairs of subgroups of a group and on distributive groups. Further on a criterion is given for ideals of a given ring to be a distributive pair of subrings.
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