New findings establish conditions for pseudo core invertibility in rings, highlighting implications for operator matrices.
We present new additive results regarding the pseudo core inverse in a ring with involution. We establish the necessary and sufficient conditions under which the sum of two pseudo core invertible elements in a ring is also pseudo core invertible. As an application, we investigate the pseudo core invertibility of operator matrices. These findings extend the additive result on pseudo core invertibility by Gao and Chen [Comm. Algebra, 46 (2018), 38-50].
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Chen et al. (2025) studied this question.
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