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Drazin-Moore-Penrose invertibility in rings. (English) Zbl 1080.15004

The authors give characterizations for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and explain the difference between these elements and EP-elements. They also generalize the results to elements for which a power has a Moore-Penrose inverse and a group inverse that are equal. At the same time they consider as an application the ring of square matrices of order \(m\) over a projective free ring \(R\) with involution such that \(R^m\) is a module of finite length, providing a new characterization for range-Hermitian matrices over the complexes.

MSC:

15A09 Theory of matrix inversion and generalized inverses
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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