<p>We study the reflexive properties of rings determined by idempotents in a more general setting. A new concept named right <i>e</i>-reflexive rings is defined and studied. This is a generalization of reflexive rings and right <i>e</i>-reversible rings. Some necessary examples and counterexamples are given. Furthermore, we consider the restriction of the right <i>e</i>-reflexivity to nilpotent elements, which strictly contains the classes of reflexive rings and right <i>e</i>-reflexive rings. Some well-known results on reflexive rings are unified and extended.</p>