Mason introduced the reflexive property for ideals. We in this thesis consider the reflexive ring property on nil ideals , introducing the concept of a nil-reflexive ring as a generalization of the reflexive ring property . We will call a ring R nil-reflexive if IJ=? implies JI=? for nil ideals I , J of R . The polynomial and the power series rings over a right Noetherian ring (or an NI ring) R are shown to be nil-reflexive if (aRb)^?=? implies aRb=? for all a , b ? N(R). We further investigate the structure of nil-reflexive rings , related to various sorts of ring extensions. Afterwards , we restrict the reflexivity to nilpotent elements , and a ring will be said to be RNP if it satisfies this restriction . The structure of RNP rings is studied in relation to the near concepts and ring extensions which have roles in ring theory .
