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

Voir la notice de l'article provenant de la source Cambridge University Press

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/}
}
TY  - JOUR
AU  - Wang, Long
AU  - Castro-Gonzalez, Nieves
AU  - Chen, Jianlong
TI  - Characterizations of Outer Generalized Inverses
JO  - Canadian mathematical bulletin
PY  - 2017
SP  - 861
EP  - 871
VL  - 60
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-080-5/
DO  - 10.4153/CMB-2016-080-5
ID  - 10_4153_CMB_2016_080_5
ER  - 
%0 Journal Article
%A Wang, Long
%A Castro-Gonzalez, Nieves
%A Chen, Jianlong
%T Characterizations of Outer Generalized Inverses
%J Canadian mathematical bulletin
%D 2017
%P 861-871
%V 60
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-080-5/
%R 10.4153/CMB-2016-080-5
%F 10_4153_CMB_2016_080_5

[1] [1] Bott, R. and Duffin, R. J., On the algebra of networks. Trans. Amer. Math. Soc. 74(1953), 99–109. Google Scholar | DOI

[2] [2] Cao, J. and Y. Xue, The characterizations and representations for the generalized inverses with prescribed idempotents in Banach algebras. Filomat 27(2013), 851–863. Google Scholar | DOI

[3] [3] Cao, J., Perturbation analysis for the generalized inverses with prescribed idempotents in Banach algebras. arxiv:1301.4314 Google Scholar

[4] [4] Castro, N.-Gonzalez, J. Chen, and L. Wang, Further results on generalized inverses in rings with involution. Electron. J. Linear Algebra 30(2015), 118–134. Google Scholar | DOI

[5] [5] Castro, N.-Gonzalez, Koliha, J. J., and Y. Wei, Perturbation oftheDrazin inverse for matrices with equal eigenprojections at zero. Linear Algebra Appl. 312(2000), no. 1–3,181-189. Google Scholar | DOI

[6] [6] Djordjevic, D. S. and Wei, Y. M., Outer generalized inverses in rings. Comm. Algebra 33(2005), no. 9, 3051-3060. Google Scholar | DOI

[7] [7] Drazin, M. P., A class of outer generalized inverses. Linear Algebra Appl. 436(2012), no. 7, 1909-1923. Google Scholar | DOI

[8] [8] Huylebrouck, D., R. Puystjens, and J. van Geel, The Moore-Penrose inverse of a matrix over a semi-simple artinian ring. Linear and Multilinear Algebra 16(1984), no. 1–4, 239–246. Google Scholar | DOI

[9] [9] ILic, D.C., Liu, X. J., and J. Zhong, On the (p, q)-outer generalized inverse in Banach algebra. Appl. Math. Comput. 209(2009), 191–196. Google Scholar | DOI

[10] [10] Kantun-Montiel, G., Outer generalized inverses with prescribed ideals. Linear Multilinear Algebra 62(2014), no. 9, 1187–1196. Google Scholar | DOI

[11] [11] Koliha, J. J. and P. Patricio, Elements of rings with equal spectral idempotents. J. Aust. Math. Soc. 72(2002), no. 1, 137–152. Google Scholar | DOI

[12] [12] Mosic, D., Djordjevic, D. S., and G. Kantun-Montiel, Image-kernel (p, q)-inverse in rings. Electron. J. Linear Algebra 27(2014), 272–283. Google Scholar | DOI

[13] [13] Patricio, P. and C. Mendes Araujo, Moore-Penrose invertibility in involutory rings: The case aaf = bbf. Linear Multilinear Algebra 58(2010), no. 3-4, 445-452. Google Scholar | DOI

[14] [14] Patricio, P. and R. Puystjens, Generalized invertibility in two semigroups of a ring. Linear Algebra Appl. 377(2004), 125-139. Google Scholar | DOI

Cité par Sources :