On reflexive and 𝐼-Ulrich modules over curve singularities

DOI10.1090/btran/96OpenAlexW4323031753MaRDI QIDQ5880154

Sarasij Maitra, Prashanth Sridhar, Hailong Dao

Publication date: 7 March 2023

Published in: Transactions of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.02641

zbMATH Keywords

conductorsreflexive modulesGorenstein ringscanonical idealtrace idealsbirational extensions\(I\)-Ulrich modules

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Structure, classification theorems for modules and ideals in commutative rings (13C05) Singularities of curves, local rings (14H20) Extension theory of commutative rings (13B02) Other special types of modules and ideals in commutative rings (13C13) Module categories and commutative rings (13C60)

Related Items

When are trace ideals finite?, The tiny trace ideals of the canonical modules in Cohen-Macaulay rings of dimension one, Reflexive modules over the endomorphism algebras of reflexive trace ideals

Cites Work

• Unnamed Item
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• Totally reflexive extensions and modules.
• Almost Gorenstein rings
• Trace ideals and centers of endomorphism rings of modules over commutative rings
• Ulrich modules over cyclic quotient surface singularities
• Remarks on quasi-Frobenius rings
• Linear maximal Cohen-Macaulay modules over strict complete intersections
• Gorenstein rings and modules with high numbers of generators
• Integrally closed ideals and type sequences in one-dimensional local rings
• One-dimensional almost Gorenstein rings
• On the integral closure of ideals
• A formula for the core of an ideal
• On the biggest maximally generated ideal as the conductor in the blowing up ring
• Trace ideals of canonical modules, annihilators of Ext modules, and classes of rings close to being Gorenstein
• Syzygies of Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings
• Trace ideals, normalization chains, and endomorphism rings
• Totally reflexive modules over rings that are close to Gorenstein
• Almost Gorenstein rings - towards a theory of higher dimension
• Correspondence between trace ideals and birational extensions with application to the analysis of the Gorenstein property of rings
• The trace of the canonical module
• Algèbre locale. Multiplicités. Cours au Collège de France, 1957-1958, rédigé par Pierre Gabriel. 2e ed.
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• Partial trace ideals and Berger's conjecture
• Gorenstein dimension and torsion of modules over commutative noetherian rings
• ULRICH IDEALS AND MODULES OVER TWO-DIMENSIONAL RATIONAL SINGULARITIES
• Weak normality and seminormality
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Maximally generated Cohen-Macaulay modules.
• Generators of reductions of ideals in a local Noetherian ring with finite residue field
• A theorem of Briançon-Skoda type for regular local rings containing a field
• Rings whose ideals are isomorphic to trace ideals
• Ulrich modules over Cohen–Macaulay local rings with minimal multiplicity
• Ulrich ideals and modules
• Stable Ideals and Arf Rings
• On seminormality