Generalized inverses of a sum in rings

• Author(s): Castro-González, N. ; Araújo, C. Mendes ; Patrício, Pedro
• Date: 2010
• Persistent ID: http://hdl.handle.net/1822/11383
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Regular element; Reflexive inverse; Drazin index; Drazin inverse; EP elements
• Document Type: Article
• Language: English

Description

Documento submetido para revisão pelos pares. A publicar em "Bulletin of the Australian Mathematical Society". ISSN 0004-9727. 82:1 (2010) 156-164. We study properties of the Drazin index of regular elements in a ring with a unity 1. We give expressions for generalized inverses of 1 − ba in terms of generalized inverses of 1 − ab. In our development we prove that the Drazin index of 1 − ba is equal to the Drazin index of 1 − ab.