IDEAS home Printed from https://ideas.repec.org/a/hin/jijmms/5232935.html
   My bibliography  Save this article

Prime Graphs of Polynomials and Power Series Over Noncommutative Rings

Author

Listed:
  • Walaa Obaidallah Alqarafi
  • Wafaa Mohammed Fakieh
  • Alaa Abdullah Altassan

Abstract

The prime graph PGR of a ring R is a graph whose vertex set consists of all elements of R. Two elements x,y∈R are adjacent in the graph if and only if xRy=0 or yRx=0. An element a∈R is called a strong zero divisor in R if ab=0 or ba=0 for some nonzero element b∈R. The set of all strong zero divisors is denoted by SR. In this paper, we study the prime graph of a ring R, considering SR as the set of vertices. In this way, we introduce the modified prime graph PG∗R. We then investigate some combinatorial properties of the prime graphs PGRx and PGRx such as completeness, diameter, and girth, where R is a noncommutative ring.

Suggested Citation

  • Walaa Obaidallah Alqarafi & Wafaa Mohammed Fakieh & Alaa Abdullah Altassan, 2025. "Prime Graphs of Polynomials and Power Series Over Noncommutative Rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2025, pages 1-8, October.
    • Handle: RePEc:hin:jijmms:5232935
    DOI: 10.1155/ijmm/5232935
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/ijmms/2025/5232935.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/ijmms/2025/5232935.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/ijmm/5232935?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:jijmms:5232935. 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.