LetK,S,Tbe subsets of a near-ringR.ThenKis (S,T)-distributive if:s(k1+k2)t=sk1t+sk2t, for eachk1,k2εK,sεS,tεT; andKis (S, T)-d.g. onXifKis (S, X)-distributive andTis contained in the additive subgroup generated byX.This paper considers υ-primitivity and the associated ℑυradicals under various such conditions, particularly whereS, T, andKare powers ofR.Natural examples which illustrate and delimit the theory are given.