Right ideals in transformation nearrings (Q2777989)

The transformation near-rings considered here are the near-ring \(M_0(G)\) of all zero-preserving mappings of a group \(G\) to itself and the near-ring \(M(G)\) of all mappings of \(G\) to itself. All near-rings considered are right near-rings. If \(G\) is finite a group, then the authors determine all right ideals of \(M_0(G)\) and show that they are principal. If in addition \(G\) is Abelian, all the right ideals of \(M(G)\) are determined and the maximal right ideals are shown to be principal. These results are applied to the near-ring of polynomials over a finite field.