IDEAS home Printed from https://ideas.repec.org/a/wsi/nmncxx/v16y2020i01ns1793005720500076.html
   My bibliography  Save this article

Event and Its Application in Algebraic Structures

Author

Listed:
  • Young Bae Jun

    (Department of Mathematics Education, College of Education, Gyeongsang National University, Jinju 52828, South Korea)

  • Seok-Zun Song

    (#x2020;Department of Mathematics, Jeju National University, Jeju 63243, South Korea)

  • Seon Jeong Kim

    (#x2021;Department of Mathematics, Natural Science of College, Gyeongsang National University, Jinju 52828, South Korea)

Abstract

The notion of eventful element and eventful set is introduced, and its application is considered in BCI and/or BCK algebras. Several properties are investigated, and (positive implicative) ideal in an eventful BCK algebra and closed ideal in an eventful BCI algebra are discussed. Given the subsets A and B of a BCI and/or BCK algebra, the eventful subset E(A,B) which consists of BCI and/or BCK events with a condition is established. Conditions for the eventful subset E(A,B) to be a (positive implicative) ideal of an eventful BCK algebra are provided, and conditions for the eventful subset E(A,B) to be a (closed) ideal of an event BCI algebra are given. An example to show that the set {0̃} is not a positive implicative ideal in an eventful BCK algebra is provided, and then the conditions for the set {0̃} to be a positive implicative ideal in an eventful BCK algebra are considered.

Suggested Citation

  • Young Bae Jun & Seok-Zun Song & Seon Jeong Kim, 2020. "Event and Its Application in Algebraic Structures," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 105-121, March.
    • Handle: RePEc:wsi:nmncxx:v:16:y:2020:i:01:n:s1793005720500076
    DOI: 10.1142/S1793005720500076
    as

    Download full text from publisher

    File URL: https://www.worldscientific.com/doi/abs/10.1142/S1793005720500076
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S1793005720500076?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:16:y:2020:i:01:n:s1793005720500076. 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.