Drazin-Moore-Penrose invertibility in rings
Characterizations are given for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and the difference between these elements and EP-elements is explained. The results are also generalized to elements for which a power has a Moore-Penrose...
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| Format: | article |
| Language: | eng |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1822/1516 |
| Country: | Portugal |
| Oai: | oai:repositorium.sdum.uminho.pt:1822/1516 |
| Summary: | Characterizations are given for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and the difference between these elements and EP-elements is explained. The results are also generalized to elements for which a power has a Moore-Penrose inverse and a group inverse that are equal. As an application we consider 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. |
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