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.
Alqahtani et al. (2026) studied this question.