On matrix near-rings

Let R be a right near-ring with identity and M_n(R) be the near-ring of n 2 n matrices over R in the sense of Meldrum and Van der Walt. In this paper, M_n(R) is said to be ssigma-generated if every n 2 n matrix A over R can be expressed as a sum of elements of X_n(R), where X_n(R)={f_ij^r | 1leqq i, jleqq n, r ? R}X_n(R)={f_{ij}^r,|,1leqq i, jleqq n, rin R}, is the generating set of M_n(R). We say that R is ssigma-generated if M_n(R) is ssigma-generated for every natural number n. The class of ssigma-generated near-rings 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 zerosymmetric abelian ssigma-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).