IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-981-10-6838-6_15.html

Transitive Filters

In: A Course in BE-algebras

Author

Listed:
  • Sambasiva Rao Mukkamala

    (MVGR College of Engineering, Department of Mathematics)

Abstract

It is a general observation in a BE-algebra that the BE-ordering $$\le $$ is reflexive but neither antisymmetric nor transitive. If the BE-algebra X is commutative, then the pair $$(X, \le )$$ is a partially ordered set. If X is transitive, then $$\le $$ satisfies only the transitive property. This is the exact reason to concentrate on the transitive property of the filters and to introduce the filters called transitive filters. It is also observed that every filter of a BE-algebra satisfies the transitive property whenever the BE-algebra is transitive. Along with the transitive property of filters, the distributive property is also studied in BE-algebras and introduced the notion of distributive and strong distributive filters in BE-algebras. It is also observed that every filter of a BE-algebra satisfies the distributive property whenever the BE-algebra is self-distributive.

Suggested Citation

  • Sambasiva Rao Mukkamala, 2018. "Transitive Filters," Springer Books, in: A Course in BE-algebras, chapter 0, pages 413-434, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-6838-6_15
    DOI: 10.1007/978-981-10-6838-6_15
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-981-10-6838-6_15. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.