S-PRIMITIVITY IN MATRIX NEAR-RINGS

Abstract

Let R be a near-ring and M_n(R) the associated near-ring of n x n matrices as defined by Meldrum and van der Walt. If R is s-primitive, then M _n(R) is s-primitive. On the other hand if M _n(R) is s-primitive, then the s-radical J _s(R) is zero. With suitable chain conditions r is a faithful M _n(R)-group of type-s if and only if is M _n(R)-isomorphic to Gⁿ for G a faithful R-group of type-s.