Weakly prime ideals in near-rings

In this short note, we introduce the notion of prime ideals in near-ring and obtain equivalent conditions for an ideal to be a weakly prime ideal. Keywords and Phrases: Near-ring, Prime ideal, M-system, Weakly prime ideal.
1. Introduction Throughout this paper, N denotes a zero-symmetric near-ring not necessarily with identity unless otherwise stated. For x [member of] N, < x > denote the ideal of N [...]