Right Jacobson Radicals For Right Near-Rings

By Korrapati Siva Prasad

The Jacobson radical is a very significant radical in rings.It is well known in ring theory that the right and left Jacobson radicals of a ring are the same but a right(left)primitive ring need not be a left(right)primitive ring.No true generalization of Wedderburn-Artin theorem of rings was developed to near-rings which involves direct product of matrix near-rings.This requires the right Jacobson radicals of near-rings. Three right Jacobson radicals are introduced and it is established that they are all Kurosh-Amitsur radicals in the class of all near-rings in which the constant part of a near-ring is an ideal of that near-ring.Their relations with the existing radicals of near-rings are presented. Also another three right Jacobson radicals are introduced and it is established that they are all Kurosh-Amitsur radicals in the class of all near-rings and are also ideal-hereditary in the class of all zero-symmetric near-rings. Semisimple classes of these Jacobson radicals are studied and some generalizations of Wedderburn-Artin theorem of rings are presented.

• Format: Paperback
• Language: English
• ISBN: 3659642355
• ISBN13: 9783659642357
• Release Date: April 2015
• Publisher: LAP Lambert Academic Publishing
• Length: 144 Pages
• Weight: 0.49 lbs.
• Dimensions: 0.3" x 6.0" x 9.0"