Completeness for concrete near-rings

In this paper a completeness criterion for near-rings over a finite group is derived using techniques from clone theory. The relationship between near-rings and clones containing the group operations of the underlying group shows that the unary parts of such clones correspond precisely to nearrings containing the identity function. Rosenberg's characterization of maximal clones is then applied to describe maximal near-rings containing the identity map, while maximal near-rings not containing the identity are described using typical near-ring methods. This finally provides us with a completeness criterion. We apply this criterion to show that if the order of F is large then with high probability the set containing a single bijection is complete. (C) 2004 Elsevier Inc. All rights reserved.