CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

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,
    Departamento Matemática Aplicada, ETSI Informática, Universidad Politécnica Madrid, 28660 Madrid, Spain
  • 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 $(b, c)$-inverse, $(b, c)$-idempotent, regularity, image-kernel $(p, q)$-inverse, ring
MSC Classifications: 15A09, 16U99 show english descriptions Matrix inversion, generalized inverses
None of the above, but in this section
15A09 - Matrix inversion, generalized inverses
16U99 - None of the above, but in this section
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/