On the Drazin index of regular elements

• Author(s): Patrício, Pedro ; Costa, A. Veloso da
• Date: 2009
• Persistent ID: http://hdl.handle.net/1822/10534
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Drazin inverse; Drazin index; Dedekind finite ring; Regular ring
• Document Type: Article
• Language: English

Description

It is known that the existence of the group inverse $a^\#$ of a ring element $a$ is equivalent to the invertibility of $a^2a^-+1-aa^-$, independently of the choice of the von Neumann inverse $a^-$ of $a$. In this paper, we relate the Drazin index of $a$ with the Drazin index of $a^2a^-+1-aa^-$. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.