Special radicals of near-rings and Γ-near-rings

It was previously shown that every special radical class R of rings induces a special radical class ρ{variant}R of Γ-rings. Amongst the special radical classes of near-rings, there are some, called the σ-special radical classes, which induce, special radical classes of Γ-near-rings by the same procedure as used in the ring case. The σ-special radicals of near-rings possess very strong hereditary properties. In particular, this leads to some new results for the equiprime and I₃ radicals.