Let R be an associate ring with involution and let a, w ∈ R. The notion of EI along an element is introduced. An element w is called EI along a if w ∥a exists and w ∥a w = ww ∥a. Its several characterizations are given by w-core inverses. Several necessary and sufficient conditions such that a # w aw and wa # w a are projections are derived. In particular, it is shown that a # w aw is a projection if and only if aw is Moore-Penrose invertible with (aw) † = a # w if and only if aw is group invertible with (aw) # = a # w. Also, wa # w a is a projection if and only if a is Moore-Penrose invertible with a † = wa # w. Then, we describe the existence of w-core inverse of a by the existence of (the unique) projection p ∈ R and idempotent q ∈ R satisfying pR = aR = awR = qR and Rq = Raw.