A study on the concept of the commutativity via nilpotent elements

The reflexive property on right ideals was initially introduced by Mason. Recently this concept was extended to many sorts of subsets in rings. We in this note confine the reflexivity to nilpotent elements, introducing the concept of an RNP ring as a generalization of the reflexive ring property. The structure of RNP rings is investigated in relation to the near concepts and ring extensions which have roles in ring theory