A non-ideal-hereditary Kurosh–Amitsur prime radical for near-rings

On the Prime Radical of Nearrings which is Kurosh-Amitsur

“…A characterization of the prime radical of near-rings was given in [5] using right modules of near-rings. With this motivation right representation of radicals of right near-ring was presented in [7] and a prime radical for near-rings, the right prime radical of type 1, was defined and studied in [6] which is a non-ideal hereditary Kurosh-Amitsur radical. This is the second known Kurosh-Amitsur prime radical of near-rings.…”