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<p>This paper investigates the finite generation of the strict closure of rings in arbitrary dimension. For a Noetherian local ring <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((R, \mathfrak m)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mo>,</mo> <mi mathvariant="fraktur">m</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, we provide a sufficient condition under which the strict closure <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation> is finitely generated as an <i>R</i>-module. Using this result, we characterize the finite generation of the strict closure over excellent rings.</p>

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When is the strict closure of rings finitely generated?

  • 期刊论文

  • 发表日期：

    2026年7月4日

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  • Ryotaro Isobe

摘要

This paper investigates the finite generation of the strict closure of rings in arbitrary dimension. For a Noetherian local ring \((R, \mathfrak m)\) ( R , m ) , we provide a sufficient condition under which the strict closure \(R^*\) R ∗ is finitely generated as an R-module. Using this result, we characterize the finite generation of the strict closure over excellent rings.