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THE LINK BETWEEN REGULARITY AND STRONG-PI-REGULARITY

Part of: Basic linear algebra

Published online by Cambridge University Press:  09 August 2010

PEDRO PATRÍCIO  and
R. E. HARTWIG
PEDRO PATRÍCIO*
Affiliation:
Departamento de Matemática e Aplicações, Universidade do Minho, 4710-057 Braga, Portugal (email: pedro@math.uminho.pt)
R. E. HARTWIG
Affiliation:
Department of Mathematics, N.C.S.U., Raleigh, NC 27695-8205, USA (email: hartwig@unity.ncsu.edu)
*
✉For correspondence; e-mail: pedro@math.uminho.pt
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Abstract

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It is shown that if all powers of a ring element a are regular, then a is strongly pi-regular exactly when a suitable word in the powers of a and their inner inverses is a unit.

Keywords

Drazin inversestrongly pi-regularDrazin index

MSC classification

Secondary: 15A09: Matrix inversion, generalized inverses
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 1 , August 2010 , pp. 17 - 22
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This research received financial support from the Research Centre of Mathematics of the University of Minho (CMAT) through the FCT Pluriannual Funding Program.

References

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