Abstract
An element a in a *-ring R has *-DMP inverse if there exists such that
and
If m = 1, then a is said to have *-gMP inverse. In this paper, we present several new characterizations of *-DMP inverses in a *-ring. We prove that a has *-DMP inverse if and only if there exists a projection
such that
and ae is nilpotent if and only if there exist
and
such that
and
Moreover, we prove that
has *-gMP inverse if and only if
for some
The corresponding new characterization of *-DMP inverse is thereby obtained.
Acknowledgement
The authors would like to thank the referee for his/her helpful suggestions for the improvement of this paper.