2011/06/09 by Norihiro Nakashima, Nakashima, Norihiro
Computer Science · Mathematics · #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13N10 #Rings and Algebras (math.RA) #Secondary 32S22 #math.RA #msc:13N10 #msc:32S22
paper · pdf · doi:10.48550/arxiv.1106.1756
arxiv created 2011/06/09 · openalex publication_date 2011/06/09 · arxiv updated 2011/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Whereas Holm proved that the ring of differential operators on a generic hyperplane arrangement is finitely generated as an algebra, the problem of its Noetherian properties is still open. In this article, after proving that the ring of differential operators on a central arrangement is right Noetherian if and only if it is left Noetherian, we prove that the ring of differential operators on a central 2-arrangement is Noetherian. In addition, we prove that its graded ring associated to the order filtration is not Noetherian when the number of the consistuent hyperplanes is greater than 1.