IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p243-d487149.html
   My bibliography  Save this article

Regular Parameter Elements and Regular Local Hyperrings

Author

Listed:
  • Hashem Bordbar

    (Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia)

  • Irina Cristea

    (Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia)

Abstract

Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring. These elements provide a deep connection between the dimension of the hyperring and its primary hyperideals. Then, our study focusses on the concept of regular local hyperring R , with maximal hyperideal M , having the property that the dimension of R is equal to the dimension of the vectorial hyperspace M M 2 over the hyperfield R M . Finally, using the regular local hyperrings, we determine the dimension of the hyperrings of fractions.

Suggested Citation

  • Hashem Bordbar & Irina Cristea, 2021. "Regular Parameter Elements and Regular Local Hyperrings," Mathematics, MDPI, vol. 9(3), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:243-:d:487149
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/3/243/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/3/243/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anastase Nakassis, 1988. "Recent results in hyperring and hyperfield theory," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-12, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christos G. Massouros & Gerasimos G. Massouros, 2023. "On the Borderline of Fields and Hyperfields," Mathematics, MDPI, vol. 11(6), pages 1-35, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christos G. Massouros & Gerasimos G. Massouros, 2023. "On the Borderline of Fields and Hyperfields," Mathematics, MDPI, vol. 11(6), pages 1-35, March.
    2. Gerasimos Massouros & Christos Massouros, 2020. "Hypercompositional Algebra, Computer Science and Geometry," Mathematics, MDPI, vol. 8(8), pages 1-33, August.
    3. Christos Massouros & Gerasimos Massouros, 2021. "An Overview of the Foundations of the Hypergroup Theory," Mathematics, MDPI, vol. 9(9), pages 1-41, April.
    4. Kaique M. A. Roberto & Kaique R. P. Santos & Hugo Luiz Mariano, 2024. "On Non-Commutative Multi-Rings with Involution," Mathematics, MDPI, vol. 12(18), pages 1-17, September.

    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:9:y:2021:i:3:p:243-:d:487149. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.