Year: 2026
Type: article
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.
Source: Mathematics
DOI: 10.3390/math14020237
Authors: Noômen Jarboui, Bana Al Subaiei
Institutions: Sultan Qaboos University, King Faisal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: King Faisal University
OpenAlex ID: W7119511079