2022/10/21 by Jason P. Bell, Bell, Jason P., Léon Burkhardt +3
Mathematics · #16A20 #16A3 #16D60 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2210.12024
openalex publication_date 2022/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Ore extensions of the form T:=R[x;σ,δ] with R a commutative integral domain that is finitely generated over a field k. We show that if T has Gelfand-Kirillov dimension less than four then a prime ideal P∈ \rm Spec(T) is primitive if and only if \P\ is locally closed in \rm Spec(T), if and only if the Goldie ring of quotients of T/P has centre that is an algebraic extension of k. We also show that there are examples for which these equivalences do not all hold for T of integer Gelfand-Kirillov dimension greater than or equal to 4.