| Abstract: | For right near-rings the left representation has always been considered the natural one. However, Hanna Neumann 6] constructed her right near-rings by writing the reduced free group on the left of the near-ring. In 2] and 8] Neumann's ideas are placed in a more general setting in the sense that right R-groups are used to define radical-like objects in the near-ring R. The right 0-radical r J 0(R) and the right half radical r J ½(R) are introduced in 2] where it is shown that for distributively generated (d.g.) near-rings R with a multiplicative identity and satisfying the descending chain condition for left R-subgroups r J 0(R) = J 2(R), the 2-radical from left representation. In this article we introduce the right 2-radical, r J 2(R) for d.g. near-rings and discuss some of its properties. In particular, we show that for all finite d.g. near-rings with identity J 2(R) = r J 2(R). |
