A CHARACTERIZATION OF THE GENERALIZED INVERSES OVER DIVISION RINGS

Peal2] shows that a sufficient and necessary condition on the existence of theMoore-Penrose inverse over any fields.Zhuang 3] generalize the result to any divisionrings.In this section we give another sufficient and necessary condition on the existence ofthe Moore-Penrose inverse over any division rings.Our result can be regarded as an im-provement of Theorem lin1].As a medium result,we also show a characterization ofthe{1,2}-inverse.