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+.
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Hartney, J.F., Rusznyak, D.S. (2005). A Right Radical for Right D.G. Near-Rings. In: Kiechle, H., Kreuzer, A., Thomsen, M.J. (eds) Nearrings and Nearfields. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3391-5_11
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DOI: https://doi.org/10.1007/1-4020-3391-5_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3390-2
Online ISBN: 978-1-4020-3391-9
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