International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 741609, 6 pages
doi:10.1155/2008/741609
Research Article
Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings
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
Received 20 August 2007; Accepted 6 November 2007
Academic Editor: Howard E. Bell
Copyright © 2008 Ravi Srinivasa Rao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.