Near-rings and partitioned groups

摘要

The near-rings of mappings arising from partitioned groups have been studied by Maxson and van der Walt ( 1994). We axiomatize the situation giving rise to these near-rings, de. ning a near-ring associated with a family of partitioned groups. This generalizes the work of Maxson and van der Walt and there are many special cases which are of interest. We develop a general structure theory for these near-rings and we also look in more detail at some special cases.