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<p>Let <i>R</i> be a commutative Noetherian ring, <i>I</i> an ideal of <i>R</i>. In this paper we show that the category of all weakly cofinite modules with respect to an ideal <i>I</i> of <i>R</i> is an Abelian subcategory of the category of <i>R</i>-modules, whenever <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10013_2025_746_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{cd}(I,R)\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>cd</mtext> <mo stretchy="false">(</mo> <mi>I</mi> <mo>,</mo> <mi>R</mi> <mo stretchy="false">)</mo> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Abelian Category of Weakly Cofinite Modules for Ideals of Cohomological Dimension One

  • 期刊论文

  • 发表日期：

    2025年4月29日

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  • Moharram Aghapournahr,
  • Gholamreza Pirmohammadi

摘要

Let R be a commutative Noetherian ring, I an ideal of R. In this paper we show that the category of all weakly cofinite modules with respect to an ideal I of R is an Abelian subcategory of the category of R-modules, whenever \(\textrm{cd}(I,R)\le 1\) cd ( I , R ) ≤ 1 .