Completeness for concrete near-rings

Journal article

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 near-rings 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 Γ is large then with high probability the set containing a single bijection is complete. © 2004 Elsevier Inc. All rights reserved.

Authors: Aichinger, E; Masulovic, D; Poschel, R; Wilson, J

• Publication status: Published
• Journal: JOURNAL OF ALGEBRA
• Volume: 279
• Issue: 1
• Pages: 61-78
• Publication date: 2004-09-01
• DOI: 10.1016/j.jalebra.2004.04.011
• ISSN: 0021-8693
• Language: English
• Keywords: near-ring; maximal clone; completeness; maximal near-ring