Left ideals and 0-primitivity in matrix near-rings

Abstract

Maximal left ideals in matrix rings were studied by Stone [ 10 ]. Similar results are not necessarily valid in the general near-ring case and one of the objectives of this paper is to study these differences. Furthermore, although much is known about 2-primitivity in general matrix near-rings (Van der Walt [ 11 ]), quite the opposite is true for 0-primitivity and the other objective of this paper is to present some results on 0-primitivity in matrix near-rings in certain restricted cases.