Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 67, 2019 - Issue 6
Submit an article Journal homepage
386
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Characterizations for pseudo core inverses in a ring with involution

Huihui ZhuSchool of Mathematics, Hefei University of Technology, Hefei, China.;CMAT-Centro de Matemática, Universidade do Minho, Braga, Portugal.Correspondence[email protected]
ORCID Iconhttp://orcid.org/0000-0002-0588-930XView further author information
ORCID Icon &
Pedro PatrícioCMAT-Centro de Matemática, Universidade do Minho, Braga, Portugal.;Departamento de Matemática e Aplicações, Universidade do Minho, Braga, Portugal.View further author information
Pages 1109-1120 | Received 03 Nov 2017, Accepted 24 Feb 2018, Published online: 15 Mar 2018

References

  • Patrício P , Puystjens R . Drazin-Moore-Penrose invertibility in rings. Linear Algebra Appl. 2004;389:159–173.
  • Malik SB , Thome N . On a new generalized inverse for matrices of an arbitrary index. Appl Math Comput. 2014;226:575–580.
  • Manjunatha Prased K , Mohana KS . Core-EP inverse. Linear Multilinear Algebra. 2014;62:792–802.
  • Malik SB , Rueda L , Thome N . The class of m-EP and m-normal matrices. Linear Multilinear Algebra. 2016;64:2119–2132.
  • Mary X . On generalized inverses and Green’s relations. Linear Algebra Appl. 2011;434:1836–1844.
  • Drazin MP . A class of outer generalized inverses. Linear Algebra Appl. 2012;436:1909–1923.
  • Baksalary OM , Trenkler G . Core inverse of matrices. Linear Multilinear Algebra. 2010;58:681–697.
  • Rakić DS , Dinčić NC , Djordjević DS . Group, Moore-Penrose, core and dual core inverse in rings with involution. Linear Algebra Appl. 2014;463:115–133.
  • Chen JL , Zhu HH , Patricio P , et al . Characterizations and representations of core and dual core inverses. Canad Math Bull. 2017;60:269–282.
  • Ferreyra DE , Levis FE , Thome N . Revisiting the core EP inverse and its extension to rectangular matrices. Quaest Math. 2017. DOI:10.2989/16073606.2017.1377779
  • Mary X , Patrício P . Generalized inverses modulo ℋ in semigroups and rings. Linear Multilinear Algebra. 2013;61:1130–1135.
  • Zhu HH . On DMP inverse and m-EP elements in rings. Linear Multilinear Algebra. 2018. DOI:10.1080/03081087.2018.1432546
  • Zhu HH , Chen JL , Patrício P , et al . Centralizer’s applications to the inverse along an element. Appl Math Comput. 2017;315:27–33.
  • Gao YF , Chen JL . Pseudo core inverses in rings with involution. Comm Algebra. 2018;46:38–50.
  • Drazin MP . Pseudo-inverses in associative rings and semigroups. Amer Math Monthly. 1958;65:506–514.
  • Penrose R . A generalized inverse for matrices. Proc Camb Phil Soc. 1955;51:406–413.
  • Zhu HH , Zhang XX , Chen JL . Centralizers and their applications to generalized inverses. Linear Algebra Appl. 2014;458:291–300.
  • Puystjens R , Gouveia MC . Drazin invertibility for matrices over an arbitrary ring. Linear Algebra Appl. 2004;385:105–116.
  • Zhu HH . Several characterizations for generalized inverses in a ring. Linear Multilinear Algebra. 2018. DOI:10.1080/03081087.2017.1353948
  • Hartwig RE . Block generalized inverses. Arch Rational Mech Anal. 1976;61:197–251.
  • Zhu HH . Further results on several types of generalized inverses. Comm Algebra. 2018. DOI:10.1080/00927872.2017.1412450
  • Drazin MP . Commuting properties of generalized inverses. Linear Multilinear Algebra. 2013;61:1675–1681.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.