IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-67696-8_8.html
   My bibliography  Save this book chapter

Quotient Semiproducts

In: Simple Relation Algebras

Author

Listed:
  • Steven Givant

    (Mills College, Department of Mathematics)

  • Hajnal Andréka

    (Alfréd Rényi Institute of Mathematics, Institute of Mathematics, Hungarian Academy of Sciences)

Abstract

Quotient semiproducts constitute a substantial generalization of the semipower construction of Chapter 4 In the latter, a single simple relation algebra is given, and bijections are used to make isomorphic copies of this base algebra in every component of a corresponding rectangular system. In the quotient semiproduct construction, there is not a single base algebra, but rather a system of base algebras, and equijections are used to make isomorphic copies, not of the base algebras, but of quotients of the base algebras. (A base algebra can, itself, be such a quotient, namely the quotient by the identity element.) Moreover, the various copies of a given base algebra need not be copies of the same quotient. This provides a good deal of flexibility in the construction, and allows for a much greater variety of structure within and between the various components of the final semiproduct than is possible in the semipower construction (Figure 8.1).

Suggested Citation

  • Steven Givant & Hajnal Andréka, 2017. "Quotient Semiproducts," Springer Books, in: Simple Relation Algebras, chapter 0, pages 263-319, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-67696-8_8
    DOI: 10.1007/978-3-319-67696-8_8
    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

    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:978-3-319-67696-8_8. 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.