A characterization of the \(J_0\)-radical in matrix near-rings with DCCL (Q1860747)

Let \(R\) be a zero symmetric right nearring with identity. If the matrix nearring \(M_n(R)\) fulfills DCCL then its maximal left ideals are the sets \((K^n:a)\), where \(a\in R^n\) and \(K\) is the maximal \(R\)-ideal of the \(R\)-subgroup of \(R\) generated by the coordinates of \(a\). Now it is easy to characterize \(J_0(M_n(R))\) as intersection of suitable ideals.