Abstract
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† 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.
Acknowledgments
The authors are grateful and express their sincere thanks to the editor and the referee for their valuable and detailed comments on the manuscript. In particular, Remarks 2.9 and 2.12 and Lemmas 3.1 and 3.3 were suggested to the authors by the referee.