The near-ring of congruence-preserving functions on an expanded group

Let V be a finite expanded group, e.g., a ring or a group. We investigate the near-ring 〈C0(V);+,∘〉 of zero-preserving congruence-preserving functions on V. We obtain some information on the structure of 〈C0(V);+,∘〉 from the lattice of ideals of V: for example, the number of maximal ideals of 〈C0(V);+,∘〉 is completely determined by the isomorphism class of the ideal lattice of V.