On ideals and primeness in the generalised group near-ring

Abstract

Le Riche, Meldrum and Van der Walt introduced the concept of a group near-ring. Thereafter, starting with an ideal in the base near-ring, they constructed two corresponding ideals in the group near-ring. Furthermore, by starting with an ideal in the group near-ring, they constructed a corresponding ideal in the base near-ring. In this we paper, we generalise both the concept of the group near-ring and the construction of the three ideals. We introduce a fourth ideal, and we investigate some relationships amongst these four ideals. We also investigate whether a prime condition placed on an R-ideal of a near-ring module implies that prime condition on the corresponding ideal in the generalised group near-ring and vice versa.