One sided x-projection, one sided x-idempotent and strongly EP elements in a *-ring

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.