IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/4148088.html
   My bibliography  Save this article

A-D3 Modules and A-D4 Modules

Author

Listed:
  • Zhanmin Zhu
  • Carmelo Antonio Finocchiaro

Abstract

Let A be a class of some right R-modules that is closed under isomorphisms, and let M be a right R-module. Then M is called A-D3 if, whenever N and K are direct summands of M with M=N+K and M/K∈A, then N∩K is also a direct summand of M; M is called an A-D4 module, if whenever M=B⊕A where B and A are submodules of M and A∈A, then every epimorphism f:B⟶A splits. Several characterizations and properties of these classes of modules are investigated. As applications, some new characterizations of semisimple Artinian rings, quasi-Frobenius rings, von Neumann regular rings, semiregular rings, perfect rings, semiperfect rings, hereditary rings, semihereditary rings, and PP rings are given.

Suggested Citation

  • Zhanmin Zhu & Carmelo Antonio Finocchiaro, 2023. "A-D3 Modules and A-D4 Modules," Journal of Mathematics, Hindawi, vol. 2023, pages 1-7, September.
    • Handle: RePEc:hin:jjmath:4148088
    DOI: 10.1155/2023/4148088
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/jmath/2023/4148088.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/jmath/2023/4148088.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/4148088?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:4148088. 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.