2024/07/09 by Oleksandra Gasanova, Jürgen Herzog, Gasanova, Oleksandra +5
Mathematics · Neuroscience · #13A30 (Primary) 05E40 (Secondary) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Mind wandering and attention #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2407.06922
openalex publication_date 2024/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an ideal I in a Noetherian ring R, we introduce and study its conductor as a tool to explore the Rees algebra of I. The conductor of I is an ideal C(I)⊂ R obtained from the defining ideals of the Rees algebra and the symmetric algebra of I by a colon operation. Using this concept we investigate when adding an element to an ideal preserves the property of being of linear type. In this regard, a generalization of a result by Valla in terms of the conductor ideal is presented. When the conductor of a graded ideal in a polynomial ring is the graded maximal ideal, a criteria is given for when the Rees algebra and the symmetric algebra have the same Krull dimension. Finally, noting the fact that the conductor of a monomial ideal is a monomial ideal, the conductor of some families of monomial ideals, namely bounded Veronese ideals and edge ideals of graphs, are determined.