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Reveals properties of core-EP orthogonal elements in rings, suggesting implications for Drazin inverses and operators.
Our motivation is to explore the concepts of the left and right core-EP orthogonality for elements of a ring with involution. In this manner, we generalize notions of one-sided core-EP orthogonality for operators and core-EP orthogonality for elements of a ring with involution. Many properties and characterizations of left and right core-EP orthogonal elements are given. As consequences, we characterize left and right core orthogonal elements. We also study equivalent conditions for additive property of the core-EP inverse and the Drazin inverse.
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Stanimirović et al. (2026) studied this question.
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