RADICALS IN GENERAL #x393;-NEAR-RINGS

摘要

TheJ2andJ3radicals for zerosymmetric #x393;-near-rings were recently defined by the author. In the present paper we define theJ2(0)andJ3(0)radicals for arbitrary #x393;-near-rings. These radicals are sirmlar to corresponding ones which were recently defined by Veldsman for near-rings. LetMbe a r-near-ring with left operator near-ringL.ThenJ#x3BA;(0)(L)+=J#x3BA; (0)(M),k. = 2,3. If A is an ideal ofM, thenJ#x3BA; (0)(A) #x2286;J#x3BA; (o)(M) #x2229;A, with equality whenk= 3 andAis left invariant.J3(0)is a Kurosh-Amitsur radical in the variety of #x393;-near-rings.