Abstract
In this paper we discuss (left) near-rings satisfying the identities:abcd=acbd,abc=bac, orabc=acb, called medial, left permutable, right permutable near-rings, respectively. The structure of these near-rings is investigated in terms of the additive and Lie commutators and the set of nilpotent elementsN (R). For right permutable and d.g. medial near-rings we obtain a “Binomial Theorem,” show thatN (R) is an ideal, and characterize the simple and subdirectly irreducible near-rings. “Natural” examples from analysis and geometry are produced via a general construction method.
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Birkenmeier, G., Heatherly, H. Medial near-rings. Monatshefte für Mathematik 107, 89–110 (1989). https://doi.org/10.1007/BF01300916
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DOI: https://doi.org/10.1007/BF01300916