(Translated by https://www.hiragana.jp/)
Module Structures on Hoops
IDEAS home Printed from https://ideas.repec.org/a/wsi/nmncxx/v20y2024i03ns1793005724500339.html
   My bibliography  Save this article

Module Structures on Hoops

Author

Listed:
  • R. A. Borzooei

    (Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran)

  • M. Sabetkish

    (Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran)

  • M. Aaly Kologani

    (Hatef Higher Education Institute, Zahedan, Iran)

Abstract

In this paper, we apply the theory of modules on hoops and introduce two concepts of modules on hoops and provide special examples and interesting results. Both concepts are correct and logical. The first concept is very close to the definition of module in abstract algebra. In this case, we investigate some important results in modules such as sub-modules and quotient structures. But if we want to investigate the relationship between hoop-modules and other modules on logical algebraic structures such as BCK-modules and MV-modules, we need to define the second definition of hoop-modules. In this case, we can get that a BCK-modules and an MV-module from any hoop-module.

Suggested Citation

  • R. A. Borzooei & M. Sabetkish & M. Aaly Kologani, 2024. "Module Structures on Hoops," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 601-619, November.
    • Handle: RePEc:wsi:nmncxx:v:20:y:2024:i:03:n:s1793005724500339
    DOI: 10.1142/S1793005724500339
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S1793005724500339
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S1793005724500339?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:wsi:nmncxx:v:20:y:2024:i:03:n:s1793005724500339. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/nmnc/nmnc.shtml .

    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.