International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 741609, 6 pages
doi:10.1155/2008/741609
Kurosh-Amitsur right Jacobson radical of type 0 for right near-rings.
Ravi Srinivasa Rao1
, K.Siva Prasad2
and T. Srinivas3
1Department of Mathematics, P.G.Centre, P.B. Siddhartha College of Arts and Science, Vijayawada-520010, Andhra Pradesh, India
2Department of Mathematics, Chalapathi Institute of Engineering and Technology, Chalapathi Nagar, Lam, Guntur-522034, Andhra Pradesh, India
3Department of Mathematics, Kakatiya University, Warangal-506009, Andhra Pradesh, India
Abstract
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 radical J0r are studied. It is shown that J0r 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. So unlike the left Jacobson radicals of types 0 and 1 of near-rings, J0r is a KA-radical in the class of all zero-symmetric near-rings. J0r is not s-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.