IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v315y2017icp27-33.html
   My bibliography  Save this article

Centralizer’s applications to the inverse along an element

Author

Listed:
  • Zhu, Huihui
  • Chen, Jianlong
  • Patrício, Pedro
  • Mary, Xavier

Abstract

In this paper, we firstly prove that the absorption law for one-sided inverses along an element holds, and derive the absorption law for the inverse along an element. We then obtain the absorption law for the inverse along different elements. Also, we prove that a left inverse of a along d coincides with a right inverse of a along d, provided that they both exist. Then, the reverse order law and the existence criterion for the inverse along an element are given by centralizers in a ring. Finally, we characterize the Moore–Penrose inverse of a regular element by one-sided invertibilities in a ring with involution.

Suggested Citation

  • Zhu, Huihui & Chen, Jianlong & Patrício, Pedro & Mary, Xavier, 2017. "Centralizer’s applications to the inverse along an element," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 27-33.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:27-33
    DOI: 10.1016/j.amc.2017.07.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317305076
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.07.046?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:27-33. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.