International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 68595, 13 pages
doi:10.1155/IJMMS/2006/68595
A radical for right near-rings: The right Jacobson radical of
type-0
1Department of Mathematics, PG Centre, PB Siddhartha College of Arts and Sciences, Vijayawada 520010, Andhra Pradesh, India
2PG Department of Mathematics, JKC College, Guntur 522006, Andhra Pradesh, India
Received 23 July 2005; Revised 19 July 2006; Accepted 25 July 2006
Copyright © 2006 Ravi Srinivasa Rao and K. Siva Prasad. 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
The notions of a right quasiregular element and right
modular right ideal in a near-ring are initiated. Based on these J0r(R), the right Jacobson radical of type-0 of a near-ring R is introduced. It is obtained that J0r is a radical map and N(R)⊆J0r(R), where N(R) is the nil radical of a near-ring R. Some characterizations of J0r(R) are given and its relation with some of the radicals is also discussed.