IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v14y2026i2p237-d1836097.html

Nagata and Serre Conjecture Rings: A Unified Pullback Perspective

Author

Listed:
  • Noômen Jarboui

    (Department of Mathematics, College of Science, Sultan Qaboos University, Al-Khod 123, Muscat P.O. Box 36, Oman)

  • Bana Al Subaiei

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

Abstract

We study the strong S -property for Nagata and Serre conjecture rings through the framework of ( T , M , D ) construction rings, providing a unified approach that streamlines and extends previous results. Our main contribution is a concise, conceptual proof showing that the strong S -property of R ( X ) versus R ⟨ X ⟩ depends solely on the transcendence degree of the residue field extension K / k , where k is the quotient field of D . This perspective yields new, transparent counterexamples to both the Malik–Mott conjecture and a question of Cahen et al., and provides a clear characterization of the catenarity of Serre conjecture rings, R ⟨ n ⟩ . The approach is based on pullback constructions and the geometric structure of prime ideals, replacing intricate case analyses with arguments driven by natural invariants.

Suggested Citation

  • Noômen Jarboui & Bana Al Subaiei, 2026. "Nagata and Serre Conjecture Rings: A Unified Pullback Perspective," Mathematics, MDPI, vol. 14(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:2:p:237-:d:1836097
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/14/2/237/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/14/2/237/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:14:y:2026:i:2:p:237-:d:1836097. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.