IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/2792450.html
   My bibliography  Save this article

Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings

Author

Listed:
  • Asima Razzaque
  • Inayatur Rehman
  • Gohar Ali

Abstract

The LA-module is a nonassociative structure that extends modules over a nonassociative ring known as left almost rings (LA-rings). Because of peculiar characteristics of LA-ring and its inception into noncommutative and nonassociative theory, drew the attention of many researchers over the last decade. In this study, the ideas of projective and injective LA-modules, LA-vector space, as well as examples and findings, are discussed. We construct a nontrivial example in which it is proved that if the LA-module is not free, then it cannot be a projective LA-module. We also construct free LA-modules, create a split sequence in LA-modules, and show several outcomes that are connected to them. We have proved the projective basis theorem for LA-modules. Also, split sequences in projective and injective LA-modules are discussed with the help of various propositions and theorems.

Suggested Citation

  • Asima Razzaque & Inayatur Rehman & Gohar Ali, 2022. "Some Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, August.
    • Handle: RePEc:hin:jjmath:2792450
    DOI: 10.1155/2022/2792450
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/jmath/2022/2792450.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/jmath/2022/2792450.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/2792450?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
    ---><---

    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:hin:jjmath:2792450. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.