Elements of rings with equal spectral idempotents

• Author(s): Patrício, Pedro ; Koliha, J. J.
• Date: 2002
• Persistent ID: http://hdl.handle.net/1822/3872
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Associative ring; Involution; Idempotent; Drazin inverse; Moore-Penrose inverse; EP element
• Document Type: Article
• Language: English

Description

In this paper we define and study a generalized Drazin inverse $x^D $ for ring elements $x$, and give a characterization of elements $a, b$ for which $aa^D = bb^D$. We apply our results to the study of EP elements of a ring with involution.