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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 68595, 13 pages

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, Andhra Pradesh 520010, India
2PG Department of Mathematics, JKC College, Guntur, Andhra Pradesh 522006, India

Received 23 July 2005; Revised 19 July 2006; Accepted 25 July 2006

Copyright © 2006 Hindawi Publishing Corporation. 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.


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.