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GENERALIZED INVERSES OF A SUM IN RINGS

Part of: Basic linear algebra

Published online by Cambridge University Press:  22 April 2010

N. CASTRO-GONZÁLEZ ,
C. MENDES-ARAÚJO  and
PEDRO PATRICIO
N. CASTRO-GONZÁLEZ*
Affiliation:
Facultad de Informática, Universidad Politécnica de Madrid, 28660 Boadilla del Monte, Madrid, Spain (email: nieves@fi.upm.es)
C. MENDES-ARAÚJO
Affiliation:
Centro de Matemática, Universidade do Minho, 4710-057 Braga, Portugal (email: clmendes@math.uminho.pt)
PEDRO PATRICIO
Affiliation:
Centro de Matemática, Universidade do Minho, 4710-057 Braga, Portugal (email: pedro@math.uminho.pt)
*
✉For correspondence; e-mail: nieves@fi.upm.es
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Abstract

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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.

Keywords

regular elementreflexive inverseDrazin indexDrazin inverseEP elements

MSC classification

Secondary: 15A09: Matrix inversion, generalized inverses
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 156 - 164
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The first author was partially supported by Project MTM2007-67232, ‘Ministerio de Educación y Ciencia’ of Spain. The second and third authors were supported by the Portuguese Foundation for Science and Technology-FCT through the POCTI research program.

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