Reflexive properties of rings determined by idempotents - Zhao, Liang; Li, Xiaojie (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 512.5We study the reflexive properties of rings determined by idempotents in a more general setting. А new concept named right $e$-reflexive rings is defined and studied. This is a generalization of reflexive rings and right $e$-reversible rings. Some necessary examples and counterexamples are given. Furthermore, we consider the restriction of the right $e$-reflexivity to nilpotent elements, which strictly contains the classes of reflexive rings and right $e$-reflexive rings.  Some well-known results on reflexive rings are unified and extended.