This work explores relationships between weak e-reflexivity, e-nilpotent rings, and their stability in various ring classes, suggesting new theoretical connections.
In this work, we establish the relationships between weak e-reversibility and weak e-semicommutativity, introducing weak e-reflexive rings as a natural generalization of reflexive and e-reflexive rings. We demonstrate that, under specific conditions, weak e-reflexivity and weak e-reversibility coincide in Baer rings, and we provide characterizations via corner subrings and semicentral idempotents. Furthermore, we introduce e-nilpotent reflexive rings and examine their structural stability and connections within the class of generalized reflexive rings. A comprehensive analysis is provided regarding the behavior of these properties under polynomial and Dorroh extensions, as well as within matrix rings and quotient structures.
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Alqahtani et al. (2026) studied this question.
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