IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i9p1407-d1642464.html
   My bibliography  Save this article

Reconstructing Classical Algebras via Ternary Operations

Author

Listed:
  • Jorge P. Fatelo

    (School of Technology and Management, Polytechnic of Leiria, 2411-901 Leiria, Portugal)

  • Nelson Martins-Ferreira

    (School of Technology and Management, Polytechnic of Leiria, 2411-901 Leiria, Portugal
    CDRSP (Centre for Rapid and Sustainable Product Development), Polytechnic of Leiria, 2411-901 Leiria, Portugal)

Abstract

Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified using ternary operations. In this context, we introduce structures that contain two constants and a ternary operation. We demonstrate that these structures are isomorphic to various significant algebraic systems, including Boolean algebras, de Morgan algebras, MV-algebras, and (near-)rings of characteristic two. Our work highlights the versatility of ternary operations in describing and connecting diverse algebraic structures.

Suggested Citation

  • Jorge P. Fatelo & Nelson Martins-Ferreira, 2025. "Reconstructing Classical Algebras via Ternary Operations," Mathematics, MDPI, vol. 13(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1407-:d:1642464
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/9/1407/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/9/1407/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:9:p:1407-:d:1642464. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.