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Characterizations of Outer Generalized Inverses

Published online by Cambridge University Press:  20 November 2018

Long Wang ,
Nieves Castro-Gonzalez  and
Jianlong Chen
Long Wang
Affiliation:
Department of Mathematics, Taizhou University, Taizhou 225300, China e-mail: [email protected]
Nieves Castro-Gonzalez
Affiliation:
Departamento Matemática Aplicada, ETSI Informática, Universidad Politécnica Madrid, 28660 Madrid, Spain e-mail: [email protected]
Jianlong Chen
Affiliation:
Department of Mathematics, Southeast University, Nanjing, 210096, China e-mail: [email protected]
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Abstract

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Let $R$ be a ring and $b,c\in R$. In this paper, we give some characterizations of the $(b,c)$-inverse in terms of the direct sum decomposition, the annihilator, and the invertible elements. Moreover, elements with equal $(b,c)$-idempotents related to their $(b,c)$-inverses are characterized, and the reverse order rule for the $(b,c)$-inverse is considered.

Keywords

15A0916U99(b, c)-inverse(b, c)-idempotentregularityimage-kernel (p, q)-inversering
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 4 , 01 December 2017 , pp. 861 - 871
Copyright
Copyright © Canadian Mathematical Society 2017

References

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