Continuous closure, axes closure, and natural closure

DOI10.1090/tran/7031zbMath1390.13031arXiv1106.3462OpenAlexW2963372222MaRDI QIDQ4604412

Melvin Hochster, Neil Epstein

Publication date: 26 February 2018

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

Full work available at URL: https://arxiv.org/abs/1106.3462

zbMATH Keywords

continuous closureaxes closurenatural closureseminormal ring.

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Valuations and their generalizations for commutative rings (13A18) Ideals and multiplicative ideal theory in commutative rings (13A15) Seminormal rings (13F45) Rings and algebras of continuous, differentiable or analytic functions (46E25) Étale and flat extensions; Henselization; Artin approximation (13B40)

Related Items (12)

\(C^m\) semialgebraic sections over the plane ⋮ Smooth selection for infinite sets ⋮ Linear equations on real algebraic surfaces ⋮ On \(C^m\) solutions to systems of linear inequalities ⋮ Unnamed Item ⋮ The Brenner-Hochster-Kollár and Whitney problems for vector-valued functions and jets ⋮ Tight closure and continuous closure ⋮ Solutions to a system of equations for \(C^m\) functions ⋮ Generators for the \(C^m\)-closures of ideals ⋮ \( \mathcal{C}^m\) solutions of semialgebraic or definable equations ⋮ Weak normalization in graded extensions and weak subintegral closure of ideals ⋮ On linear equations with polynomial coefficients

Cites Work

• Progress in commutative algebra 2. Closures, finiteness and factorization
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• Seminormal rings and weakly normal varieties
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• Some properties of weakly normal varieties
• F-Regularity, Test Elements, and Smooth Base Change
• Continuous Solutions of Linear Equations
• On seminormality
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