One-sided w-core inverses in rings with an involution

This paper contributes to define one-sided versions of `w-core inverse' introduced by the writer. Given any *-ring R and a, w is an element of R, a is called right w-core invertible if there exists some x is an element of R satisfying awxa = a, awx(2) = x and awx = (awx)*. Several characterizations for this type of generalized inverses are given, and it is shown that a is right w-core invertible if and only if a is right w(aw)(n-1)-core invertible if and only if there exists a Hermitian element p such that pa = 0 and p + (aw)(n) is right invertible for any integer n >= 1, in which case, the expression of right w-core inverses is given. Finally, it is proved that right w-core inverses are instances of right inverses along an element, right (b, c)-inverses and right annihilator (b, c)-inverses. As an application, the characterization for the Moore- Penrose inverse is given.