Characterizations and representations of core and dual core inverses
  In this paper, double commutativity and the reverse order law for the core inverse are considered. Then, new characterizations of the Moore-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. 
Jianlong Chen, Huihui Zhu, Pedro Patricio, Yulin Zhang
math.RA