Abstract
Let R be a unital -ring. In this paper, we give several characterizations for the pseudo core and dual pseudo core inverses of an element by units in R. Moreover, their relations with
-DMP are obtained. As a special case, the existence criteria for EP elements (
-DMP with index 1) are given. Then, the double commutant property of hybrid (b, c)-inverses is considered. Finally, the relations of the inverse along an element and the hybrid (b, c)-inverse, the (dual) pseudo core inverses and the hybrid (b, c)-inverse are investigated.
Acknowledgements
The authors are highly grateful to the referee for his/her valuable comments and suggestions which greatly improved this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.