By a near-ring we mean a right near-ring.J0r, the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radicalJ0rare studied. It is shown thatJ0ris a Kurosh-Amitsur radical (KA-radical) in the variety of all near-ringsR, in which the constant partRcofRis an ideal ofR. So unlike the left Jacobson radicals of types 0 and 1 of near-rings,J0ris a KA-radical in the class of all zero-symmetric near-rings.J0ris nots-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.

Near-rings considered are right near-rings. Let ν ∈ {1, 2}. J r ν , the right Jacobson radical of type-ν, was introduced for near-rings by the first and second authors. In this paper properties of these radicals J r ν are studied. It is shown that J r ν is a Kurosh-Amitsur radical (KA-radical) in the variety of all near-rings R in which the constant part Rc of R is an ideal of R. Thus, unlike the left Jacobson radical of type-1 of near-rings, J r 1 is a KA-radical in the class of all zero-symmetric near-rings. J r ν is not s-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings. Mathematics Subject Classification (2000). Primary 16Y30.Keywords. Right R-groups of type-1 and 2, right primitive ideals of type-1 and 2, right Jacobson radicals of type-1 and 2.

No abstract

No abstract

No abstract