Abstract
We show that every near-ring containing a multiplicative right identity can be described as a centralizer near-ring with sandwich multiplication. Using this result we characterize planar near-rings and near-rings solving the equation xa=c in terms of such centralizer near-rings with sandwich multiplication. We also get results on primitive near-rings and on minimal left ideals in primitive near-rings.
This work has been supported by grant P15691 of the Austrian National Science Fund (FWF)
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Wendt, G. (2005). Planar Near-Rings, Sandwich Near-Rings and Near-Rings with Right Identity. In: Kiechle, H., Kreuzer, A., Thomsen, M.J. (eds) Nearrings and Nearfields. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3391-5_15
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DOI: https://doi.org/10.1007/1-4020-3391-5_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3390-2
Online ISBN: 978-1-4020-3391-9
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