Geodesic
Characterizations of Outer Generalized Inverses
Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 861-871

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DOI

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.
DOI : 10.4153/CMB-2016-080-5
Mots-clés : 15A09, 16U99, (b, c)-inverse, (b, c)-idempotent, regularity, image-kernel (p, q)-inverse, ring 
Wang, Long; Castro-Gonzalez, Nieves; Chen, Jianlong. Characterizations of Outer Generalized Inverses. Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 861-871. doi: 10.4153/CMB-2016-080-5
@article{10_4153_CMB_2016_080_5,
     author = {Wang, Long and Castro-Gonzalez, Nieves and Chen, Jianlong},
     title = {Characterizations of {Outer} {Generalized} {Inverses}},
     journal = {Canadian mathematical bulletin},
     pages = {861--871},
     year = {2017},
     volume = {60},
     number = {4},
     doi = {10.4153/CMB-2016-080-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-080-5/}
}
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