One-sided core-EP orthogonal elements in a ring with involution

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.