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Characterizations and Representations of Core and Dual Core Inverses

Published online by Cambridge University Press:  20 November 2018

Jianlong Chen ,
Huihui Zhu ,
Pedro Patricio  and
Yulin Zhang
Jianlong Chen
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, China. e-mail: jlchen@seu.edu.cn, ahzhh08@sina.com
Huihui Zhu
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, China. e-mail: jlchen@seu.edu.cn, ahzhh08@sina.com CMAT-Centro de Matemática, Universidade do Minho, Braga 4710-057, Portugal
Pedro Patricio
Affiliation:
Departamento de Matemática e Aplicações, Universidade do Minho, Braga 4710-057, Portugal. e-mail: pedro@math.uminho.pt, zhang@math.uminho.pt CMAT-Centro de Matemática, Universidade do Minho, Braga 4710-057, Portugal
Yulin Zhang
Affiliation:
Departamento de Matemática e Aplicações, Universidade do Minho, Braga 4710-057, Portugal. e-mail: pedro@math.uminho.pt, zhang@math.uminho.pt CMAT-Centro de Matemática, Universidade do Minho, Braga 4710-057, Portugal
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Abstract

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In this paper, double commutativity and the reverse order law for the core inverse are considered. Then new characterizations of the Moore–Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore, the characterizations and representations of the core and dual core inverses of a regular element are considered.

Keywords

15A0915A23regularitiesgroup inversesMoore-Penrose inversescore inversesdual core inversesDedekind-finite rings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 2 , 01 June 2017 , pp. 269 - 282
Copyright
Copyright © Canadian Mathematical Society 2017

References

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