Volume 33, No. 4, pp. 787-801, October 2007
Abstract. In this paper two more radicals B and B are introduced for near-rings which generalize the Brown-McCoy radical of rings. It is proved that B is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings but it is not a KA-radical in the class of all near-rings. Moreover, B is a KA-radical in the class of all near-rings and for a near-ring R, B (I) B (R) I for all ideals I of R and the equality holds if I is a left invariant ideal of R.
Received September 5, 2006; revised February 20, 2007.
AMS Subject Classification. 16Y30.
Key words. Brown-McCoy radicals of near-rings, weakly G-regular elements of type-, weakly -semi-nilpotent elements.