Characterizations and Representations of Core and Dual Core Inverses in rings

In this paper, double commutativity and the reverse order law for the core inverse are considered._en new characterizations of theMoore–Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore, the characterizations and representations of the core and dual core inverses of a regular element are considered.National Natural Science Foundation of China (No.11371089). FCT project UID-MAT-00013/2013