A generalization of strongly regular near-rings (Q1262380)

All near rings N considered are (right) zerosymmetric. N is said to be s- weakly regular if for each a in N, \(a=xa\) for some x in \(<a^ 2>\), the principal ideal generated by \(a^ 2\). This paper gives several equivalent conditions for N to be s-weakly regular. In particular, an s- weakly regular near-ring N is strongly regular if and only if every N- subgroup of N is an ideal.