Abstract.
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 R c 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.
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Received: April 1, 2007. Revised: July 11, 2007.
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Srinivasa Rao, R., Siva Prasad, K. & Srinivas, T. Kurosh–Amitsur Right Jacobson Radicals of Type-1 and 2 for Right Near-Rings. Result. Math. 51, 309–317 (2008). https://doi.org/10.1007/s00025-007-0280-2
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DOI: https://doi.org/10.1007/s00025-007-0280-2