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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T_{R}(M)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mi>R</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> be a tensor ring with respect to an <i>N</i>-nilpotent <i>R</i>-bimodule <i>M</i>. We first give a characterization for FP-injective modules over <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(T_{R}(M)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mi>R</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> under some mild conditions. We then apply this result to describe explicitly Ding injective modules over <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(T_{R}(M)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mi>R</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Some applications to trivial ring extensions and Morita context rings are given.</p>

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FP-Injective Modules and Ding Injective Modules Over Tensor Rings

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Aizhu Li,
  • Li Liang

摘要

Let \(T_{R}(M)\) T R ( M ) be a tensor ring with respect to an N-nilpotent R-bimodule M. We first give a characterization for FP-injective modules over \(T_{R}(M)\) T R ( M ) under some mild conditions. We then apply this result to describe explicitly Ding injective modules over \(T_{R}(M)\) T R ( M ) . Some applications to trivial ring extensions and Morita context rings are given.