Matrix near-rings and 0-primitivity

In this article, we study the implication of the primitivity of a matrix near-ring ${mathbb{M}_n(R) (n >1 )}${mathbb{M}_n(R) (n >1 )} and that of the underlying base near-ring R. We show that when R is a zero-symmetric near-ring with identity and mathbbM_n(R){mathbb{M}_n(R)} has the descending chain condition on mathbbM_n(R){mathbb{M}_n(R)}-subgroups, then the 0-primitivity of mathbbM_n(R){mathbb{M}_n(R)} implies the 0-primitivity of R. It is not known if this is true when the descending chain condition on mathbbM_n(R){mathbb{M}_n(R)} is removed. On the other hand, an example is given to show that this is not true in the case of generalized matrix near-rings.