This article investigates x-projection and x-idempotent elements in -rings, highlighting their relationships and equivalent conditions.
In this article, we present the concept of one sided x-projection, explore and investigate left and right x-projection elements, and introduce new characterizations of one sided x-idempotent elements in a +-ring. We also propose numerous equivalent conditions for left x-projections within a given ring. Next, several equivalent conditions about Hermitian, one sided x-projection, one sided x-idempotent, and strongly EP elements in a +-ring are given.
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Gadelseed et al. (2025) studied this question.
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