IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-81-322-1599-8_5.html
   My bibliography  Save this book chapter

Ideals of Rings: Introductory Concepts

In: Basic Modern Algebra with Applications

Author

Listed:
  • Mahima Ranjan Adhikari

    (Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC))

  • Avishek Adhikari

    (University of Calcutta, Department of Pure Mathematics)

Abstract

Chapter 5 continues the study of theory of rings, and introduces the concept of ideals which generalize many important properties of integers. Ideals and homomorphisms of rings are closely related. Like normal subgroups in the theory of groups, ideals play an analogous role in the study of rings. The real significance of ideals in a ring is that they enable us to construct other rings which are associated with the first in a natural way. Commutative rings and their ideals are closely related. Their relations develop ring theory and are applied in many areas of mathematics, such as number theory, algebraic geometry, topology, and functional analysis. In this chapter basic properties of ideals are discussed and explained with interesting examples. Ideals of rings of continuous functions and the Chinese Remainder Theorem for rings with their applications are also studied. Finally, applications of ideals to algebraic geometry Hilbert’s Nullstellensatz theorem, and the Zariski topology are discussed in this chapter.

Suggested Citation

  • Mahima Ranjan Adhikari & Avishek Adhikari, 2014. "Ideals of Rings: Introductory Concepts," Springer Books, in: Basic Modern Algebra with Applications, edition 127, chapter 0, pages 203-236, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1599-8_5
    DOI: 10.1007/978-81-322-1599-8_5
    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:978-81-322-1599-8_5. 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.