Tight closure commutes with localization in binomial rings

DOI10.1090/S0002-9939-00-05626-4zbMath0966.13004arXivmath/0209174OpenAlexW2143919654MaRDI QIDQ4523187

Karen E. Smith

Publication date: 8 January 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209174

zbMATH Keywords

Gröbner basistight closurelocalizationbinomial ideals

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Rings of fractions and localization for commutative rings (13B30)

Related Items (5)

Ideals in a perfect closure, linear growth of primary decompositions, and tight closure ⋮ A dual to tight closure theory ⋮ Tight closure does not commute with localization ⋮ Localization of tight closure in two-dimensional rings ⋮ The blowup closure of a set of ideals with applications to \(TI\) closure.

Cites Work

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• The complexity of Frobenius powers of ideals
• Hilbert-Kunz function of monomial ideals and binomial hypersurfaces
• Binomial ideals
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Localization of tight closure and modules of finite phantom projective dimension.
• Linear Bounds on Growth of Associated Primes

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