This research introduces right e-reflexive rings and extends concepts in reflexive rings and nilpotent elements.
UDC 512.5 We 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.
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Zhao et al. (2025) studied this question.
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