When is the canonical conductor minimal?

2025/09/26 by Özgür Esentepe, Esentepe, Özgür
Computer Science · Engineering · Materials Science · #Advanced Mathematical Modeling in Engineering #Commutative Algebra (math.AC) #Control and Stability of Dynamical Systems #FOS: Mathematics #High voltage insulation and dielectric phenomena

paper · pdf · doi:10.48550/arxiv.2509.22966

openalex publication_date 2025/09/26 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

For a one dimensional analytically unramified Cohen-Macaulay local ring R, the blowup algebra of the canonical ideal is a module finite birational extension. The conductor of this extension always contains the conductor of R. We study the case when there is equality. This is the case where R is far from being almost Gorenstein. We study this property within the landscape of numerical semigroup rings and local Arf rings.

Citations

• On conductor submonoids of factorial monoids
• Ulrich split rings
• On the set of trace ideals of a Noetherian ring
• The tiny trace ideals of the canonical modules in Cohen-Macaulay rings of dimension one
• Stable trace ideals and applications
• Reflexive modules, self-dual modules and Arf rings
• On reflexive and I-Ulrich modules over curve singularities
• The reduction number of canonical ideals
• Trace ideals, normalization chains, and endomorphism rings
• Rings whose ideals are isomorphic to trace ideals
• Syzygies of Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings
• Almost Gorenstein rings - towards a theory of higher dimension -
• Almost Gorenstein rings

Related

• Finite Birational extension with stable conductor
• Optimal Parametrizations and Valuations
• Integral closure of 1-dimensional rings
• Finite generation of a canonical ring
• Asymptotic for the number of star operations on one-dimensional Noetherian domains