A Right Radical for Right D.G. Near-Rings

John F.T. Hartney () and Danielle S. Rusznyak ()
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John F.T. Hartney: University of South Africa
Danielle S. Rusznyak: University of the Witwatersrand

A chapter in Nearrings and Nearfields, 2005, pp 225-234 from Springer

Abstract: Abstract Rahbari embarked on developing a right representation theory for right d.g. near-rings and proved interesting right structure theorems. Our main focus is connections between left and right representation. We discuss a Jacobson-type radical, rJ0(R), for right d.g. near-rings. The radical rJ0(R) is defined using annihilators of certain d.g. right R-groups which are the equivalent of type-0 R-groups from left representation. We then explore connections in near-rings with suitable chain conditions between rJ0(R), the (left) radicals and the intersection of all maximal right ideals, denoted rJ1/2(R). In particular we prove that J2(R) = rJ0(R) for near-rings R satisfying the descending chain condition for left R-subgroups of R+.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-3391-9_11

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DOI: 10.1007/1-4020-3391-5_11

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