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# Characterizations of Outer Generalized Inverses

Published:2017-01-12
Printed: Dec 2017
• Long Wang,
Department of Mathematics, Southeast University, Nanjing, 210096, China
• Nieves Castro-Gonzalez,
• Jianlong Chen,
Department of Mathematics, Southeast University, Nanjing, 210096, China
 Format: LaTeX MathJax PDF

## Abstract

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: $(b, c)$-inverse, $(b, c)$-idempotent, regularity, image-kernel $(p, q)$-inverse, ring
 MSC Classifications: 15A09 - Matrix inversion, generalized inverses 16U99 - None of the above, but in this section

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