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<p>Let&#xa0;<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R\)</EquationSource> </InlineEquation>&#xa0;be a commutative Noetherian ring with identity (not necessarily local), and let <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak {a}\)</EquationSource> </InlineEquation> be a proper ideal of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(R\)</EquationSource> </InlineEquation>. We investigate the invariance of certain classes of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathfrak {a}\)</EquationSource> </InlineEquation>-relative Cohen-Macaulay modules under pure ring homomorphisms and ring homomorphisms of finite flat dimension. Our results generalize several existing results in the literature on homological modules.</p>

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Relative Cohen-Macaulay Modules under Ring Homomorphisms

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Parisa Pourghobadian,
  • Kamran Divaani-Aazar,
  • Ahad Rahimi

摘要

Let  \(R\)  be a commutative Noetherian ring with identity (not necessarily local), and let \(\mathfrak {a}\) be a proper ideal of \(R\) . We investigate the invariance of certain classes of \(\mathfrak {a}\) -relative Cohen-Macaulay modules under pure ring homomorphisms and ring homomorphisms of finite flat dimension. Our results generalize several existing results in the literature on homological modules.