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Abstract
Let R be a ring with involution. In this paper, we extend the notions of m-EP matrices and m-EP operators to an arbitrary ring case. A number of new characterizations of m-EP elements in rings are presented. In particular, the existence criteria for 1-EP (i.e. EP) elements are obtained by means of the group inverse, Moore–Penrose inverse, and core inverse. Some properties of 2-EP are also given.
Acknowledgements
The authors would like to thank the referees for their helpful suggestions for the improvement of this paper.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This research was supported by the National Natural Science Foundation of China [grant number 11371089]; the Natural Science Foundation of Jiangsu Province [grant number BK20141327]; the Fundamental Research Funds for the Central Universities and the Foundation of Graduate Innovation Program of Jiangsu Province [grant number KYZZ15-0049]; the Portuguese Funds through FCT-‘Fundação para a Ciência e a Tecnologia’, within the project [grant number UID/MAT/00013/2013].