Abstract
The definition of the group near-ring R[G] of the near-ring R over the group G as a near-ring of mappings from R (G) to itself is due to Le Riche et al. (Arch Math 52:132–139, 1989). In this paper we consider the augmentation ideal Δ of R[G]. If the exponent of G is not 2, then the structure of ΔR (G) is determined in terms of commutators and distributors. This is then used to show that Δ is nilpotent if and only if R is weakly distributive, has characteristic p n for some prime p and G is a finite p-group for the same prime p.
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Communicated by D. Segal.
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Meldrum, J.D.P., Meyer, J.H. The augmentation ideal in group near-rings. Monatsh Math 156, 313–323 (2009). https://doi.org/10.1007/s00605-009-0100-8
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DOI: https://doi.org/10.1007/s00605-009-0100-8