The prime radical in near-rings (Q789494)

The near-rings considered are zero-symmetric right near-rings. The authors define a subset M of the near-ring N to be an m\({}^*\)-system if for any a,\(b\in M\), there exists \(b_ 1\) in the ideal generated by b such that \(ab_ 1\in M\). They use this definition to characterize the prime radical of an ideal and of the near-ring in terms of \(m^*\)- systems and \(m^*\)-sequences, following the work of \textit{A. P. J. van der Walt} [Arch. Math. 15, 408-414 (1964; Zbl 0125.010)].