The characterizations of one-sided generalized inverses

In this article, some characterizations of one-sided generalized inverses are investigated. Let R be a *-ring and It is shown that for a* is right invertible if and only if In particular, the expression of a(dagger) are given whenever Moreover, it is also proven that if and only if is right invertible along a if and only if is right invertible along a, where n is an arbitrary positive integer. Finally, we present some characterizations of by using projections and units.