IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4614-5292-8_12.html
   My bibliography  Save this book chapter

A Brief History of Order Ideals

In: Commutative Algebra

Author

Listed:
  • E. Graham Evans

    (University of Illinois at Urbana Champaign, Department of Mathematics)

  • Phillip Griffith

    (University of Illinois at Urbana Champaign, Department of Mathematics)

Abstract

The notion of order ideal is no doubt implicit in a paper by Serre in 1958 on free summands of projective modules. A formal definition is given by Bass. However, any algebraist contemplating the question, “on what locus of prime ideals in Spec(R) does an element e in a module E generate a free summand?”, has in fact encountered the concept of an order ideal. In the account on order ideals and their applications in this paper, it is our intent to elaborate on four basic theorems - as we see them - that give insight into the height properties of these ideals. We do this both from a historical view as well as a view of their utility.

Suggested Citation

  • E. Graham Evans & Phillip Griffith, 2013. "A Brief History of Order Ideals," Springer Books, in: Irena Peeva (ed.), Commutative Algebra, edition 127, pages 393-417, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-5292-8_12
    DOI: 10.1007/978-1-4614-5292-8_12
    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:978-1-4614-5292-8_12. 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.