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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathfrak {\textrm{a}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext mathvariant="fraktur">a</mtext> </math></EquationSource> </InlineEquation> be an ideal of a commutative Noetherian ring <i>R</i>. In this paper, we provide some equivalent conditions for the category of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak {\textrm{a}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext mathvariant="fraktur">a</mtext> </math></EquationSource> </InlineEquation>-cofinite modules being an Abelian subcategory of the category of all <i>R</i>-modules. This result provides a solution for the second problem of R. Hartshorne in [<i>Affine duality and cofiniteness</i>, Invent. Math. <b>9</b>(1970), 145-164].</p>

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When the category of cofinite modules with respect to an ideal is Abelian?

  • 期刊论文

  • 发表日期：

    2025年5月17日

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  • Kamal Bahmanpour

摘要

Let \(\mathfrak {\textrm{a}}\) a be an ideal of a commutative Noetherian ring R. In this paper, we provide some equivalent conditions for the category of \(\mathfrak {\textrm{a}}\) a -cofinite modules being an Abelian subcategory of the category of all R-modules. This result provides a solution for the second problem of R. Hartshorne in [Affine duality and cofiniteness, Invent. Math. 9(1970), 145-164].