On a Question of J. H. Meyer.

In this paper, we present a partial solution to the following question of J. H. Meyer (Meyer, J. H. (1986). Matrix Near-Rings. Ph.D. dissertation, University of Stellenbosch, South Africa, Prob. 11): Find a necessary and sufficient condition for a near-ring to be isomorphic to a matrix near-ring. In fact, three characterization results for abstract affine matrix near-rings are given. As a corollary, we get that, for each n ≥ 2, the class of all n × n matrix near-rings over abstract affine near-rings is finitely axiomatizable. [ABSTRACT FROM AUTHOR]