On matrix near-rings

Let R be a right near-ring with identity and M-n(R) be the near-ring of n x n matrices over R in the sense of Meldrum and Van der Walt. In this paper, M-n(R) is said to be or-generated if every n x n matrix A over R can be ex pressed as a sum of elements of X-n(R), where X-n(R) = {f(ij)(r)\1 less tha n or equal to i, j less than or equal to n, r is an element of R}, is the g enerating set of M-n(R). We say that R is or-generated if M-n(R) is sigma - generated for every natural number n, The class of sigma -generated near-ri ngs contains distributively generated and abstract affine near-rings. It is shown that this class admits homomorphic images. For abelian near-rings R, we prove that the zerosymmetric part of R is a ring, so the class of zeros ymmetric abelian or-generated near-rings coincides with the class of rings. Further, for every n, there is a bijection between the two-sided subgroups of R and those of M-n(R).