On some Radicals in Near-rings with a Defect of Distributivity

Vučić Dašić

We consider some properties of the radical $J_2(R)$ and the Levitzki radical $L(R)$ in a near-ring $R$ with a defect of distributivity. With and additional assumption that the defect $D$ of $R$ is nilpotent or $D$ is contained in the commutator subgroup of $(R,+)$ we generalize some results of Freidman [6, Theorems 1,2], and of Beidleman [1, Th.~16]. Also, we give a slight version of the Theorem 2.5 of [{\bf 3}]. By using the notation of a relative defect, we consider some properties of minimal nonnilpotent $R$-subgroups and we generalize some results of Beidleman [2, Theorems 2.4, 2.6, 2.7, 3.1].