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<p>We show that the prime spectrum of the complete integral closure <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1257_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(D^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>D</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation> of a Prüfer domain <i>D</i> is completely determined by the Zariski topology on the spectrum <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1257_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\,\textrm{Spec}\,}}(D)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mspace width="0.166667em" /> <mtext>Spec</mtext> <mspace width="0.166667em" /> </mrow> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of <i>D</i>.</p>

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The complete integral closure of a Prüfer domain is a topological property

  • 期刊论文

  • 发表日期：

    2025年6月13日

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  • Dario Spirito

摘要

We show that the prime spectrum of the complete integral closure \(D^*\) D ∗ of a Prüfer domain D is completely determined by the Zariski topology on the spectrum \({{\,\textrm{Spec}\,}}(D)\) Spec ( D ) of D.