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<p>Let <i>R</i> be a commutative Noetherian ring, and let <i>C</i> be a semidualizing <i>R</i>-module. The present paper aims at studying some properties of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_498_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="95" /> </InlineMediaObject> <EquationSource Format="TEX">\({\textrm{Hom}_{\textrm{R}}}(C, M)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>Hom</mtext> <mtext>R</mtext> </msub> <mrow> <mo stretchy="false">(</mo> <mi>C</mi> <mo>,</mo> <mi>M</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_498_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\(C \otimes _{R} M\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>C</mi> <msub> <mo>⊗</mo> <mi>R</mi> </msub> <mi>M</mi> </mrow> </math></EquationSource> </InlineEquation> where <i>M</i> is a non-zero finitely generated <i>R</i>-module. Also, we investigate other versions of depth formula for relative Tor-independent modules with respect to <i>C</i>. Finally, we establish relative versions of Ischebeck and Chouinard formulas for <i>R</i>-modules of finite relative homological dimensions with respect to <i>C</i>.</p>

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Relative versions of depth, Ischebeck, and Chouinard formulas with respect to a semidualizing module

  • 期刊论文

  • 发表日期：

    2025年2月18日

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  • Maryam Salimi,
  • Elham Tavasoli

摘要

Let R be a commutative Noetherian ring, and let C be a semidualizing R-module. The present paper aims at studying some properties of \({\textrm{Hom}_{\textrm{R}}}(C, M)\) Hom R ( C , M ) and \(C \otimes _{R} M\) C ⊗ R M where M is a non-zero finitely generated R-module. Also, we investigate other versions of depth formula for relative Tor-independent modules with respect to C. Finally, we establish relative versions of Ischebeck and Chouinard formulas for R-modules of finite relative homological dimensions with respect to C.