Applications of primeness in near rings to Malone trivial near rings. (Q2911137)

A `Malone trivial near-ring' is a near-ring \(N\) for which there is a subset \(S\subseteq N\setminus\{0\}\) such that for all \(a,b\in N\), \(ab=a\) if \(b\in S\) and \(ab=0\) if \(b\notin S\). The authors study relationships between such near-rings and near-rings satisfying properties of being right (left) permutable, medial, left (right) self-distributive, \(3\)-prime and/or completely prime. Although not mentioned, it seems that they only consider the more restricted Malone trivial near-rings with \(S=N\setminus\{0\}\).