Closure-interior duality over complete local rings

DOI10.1216/rmj.2021.51.823zbMath1477.13047arXiv1909.05739OpenAlexW3196215191MaRDI QIDQ1983212

Rebecca R. G., Neil Epstein

Publication date: 10 September 2021

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.05739

zbMATH Keywords

torsiontraceclosure operationtest idealtight closureMatlis dualityintegral closurecomplete local ringsinterior operation

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Complete rings, completion (13J10) Torsion modules and ideals in commutative rings (13C12) Module categories and commutative rings (13C60)

Related Items (3)

Characteristic-free test ideals ⋮ Nakayama closures, interior operations, and core-hull duality -- with applications to tight closure theory ⋮ Integral closure, basically full closure, and duals of nonresidual closure operations

Cites Work

• Closure operations that induce big Cohen-Macaulay modules and classification of singularities
• Criteria for flatness and injectivity
• Trace ideals and centers of endomorphism rings of modules over commutative rings
• Tight closure does not commute with localization
• Tight closure of parameter ideals
• The direct factor conjecture
• Relative homological algebra
• Co-localization, co-support and local homology
• On the commutation of the test ideal with localization and completion
• A guide to closure operations in commutative algebra
• A characterization of closure operations that induce big Cohen-Macaulay modules
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• On a generalization of test ideals
• Test Ideals in Local Rings
• A dual to tight closure theory
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