Abstract
Let R be a -ring. In this article, we introduce good
-clean elements and left
-suitable elements in R, respectively. An element
is good
-clean if it can be written as the sum of a projection and a unitary element. An element
is left
-suitable if there exists a projection
such that
Several properties of them are given and their characterizations are derived by the solvability of the Sylvester equation
in a ring. Finally, we use generalized inverses to give the existence criterion of left
-suitable elements.
Acknowledgments
The authors are highly grateful to the referee for his/her valuable comments on this article.