Characterizations of *-DMP matrices over rings

Let R be a ring with involution ∗ . Rm×n denotes the set of all m× n matrices over R . In this paper, we give a characterization of the pseudo core inverse of A ∈ Rn×n in the form of A = GDH , Nr(G) = 0, Nl(H) = 0, D = D = D∗ , where Nl(A) = {x ∈ R1×m|xA = 0} and Nr(A) = {x ∈ Rn×1 | Ax = 0}. Then we obtain necessary and sufficient conditions for A ∈ Rn×n , in the form of A = GDH , Nr(G) = 0, Nl(H) = 0, D = D = D∗ , to be *-DMP. If R is a principal ideal domain (resp. semisimple Artinian ring), then matrices expressed as that form include all n × n matrices over R .