Planar near-rings, sandwich near-rings and near-rings with right identity

We show that every near-ring containing a multiplicative right identity can be described as a centralizer near-ring with sandwich multiplication. Using this result we characterize planar near-rings and near-rings solving the equation xa=c in terms of such centralizer near-rings with sandwich multiplication. We also get results on primitive near-rings and on minimal left ideals in primitive near-rings, 2000 Mathematics Subject Classification: 16Y30.