Drazin-Moore-Penrose invertibility in rings

• Autor(es): Patrício, Pedro ; Puystjens, Roland
• Data: 2004
• Identificador Persistente: http://hdl.handle.net/1822/1516
• Origem: RepositóriUM - Universidade do Minho
• Assunto(s): Drazin; Moore-Penrose; Generalized inverses; EP elements; Core nilpotent decomposition; Fitting decomposition
• Tipo de Documento: Artigo
• Idioma: Inglês

Descrição

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.