2025/02/20 by Liping Li, Li, Liping, Yinhe Peng +2 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2502.14306
openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be a commutative Noetherian ring, and k[S] the polynomial ring whose indeterminates are parameterized by elements in a set S. We show that k[S] is Noetherian up to highly homogenous actions of groups. In particular, there is a special linear order \leqslant on infinite S such that k[S] is Noetherian up to actions of Aut(S, \leqslant), and the existence of such a linear order for every infinite set is equivalent to the axiom of choice. These Noetherian results are proved via a sheaf theoretic approach based on Artin's theorem, the work of Nagel-Römer, and a classification of highly homogenous groups by Cameron.