The Brown-McCoy radical
is known to be an ideal-hereditary Kurosh-Amitsur radical in the variety of zerosymmetric near-rings. We define the Brown-McCoy and simplical radicals,
, respectively, for zerosymmetric Γ-near-rings. Both
are ideal-hereditary Kurosh-Amitsur radicals in that variety. IfM is a zerosymmetric Γ-near-ring with left operator near-ringL, it is shown that
, with equality ifM has a strong left unity.
is extended to the variety of arbitrary near-rings, and
are extended to the variety of arbitrary Γ-near-rings, in a way that they remain Kurosh-Amitsur radicals. IfN is a near-ring andA ⊲N, then
, with equality ifA if left invariant.