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<p>In this paper, we consider Cartan–Eilenberg Gorenstein complexes with respect to duality pairs. Using the properties of duality pairs, we investigate Cartan–Eilenberg Gorenstein complexes. Moreover, we establish a relationship between Cartan–Eilenberg Gorenstein <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\mathscr{X}, \, \mathscr{Y})\)</EquationSource> </InlineEquation>-complexes and their terms for a duality pair <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((\mathscr{X}, \, \mathscr{Y})\)</EquationSource> </InlineEquation> of modules. Based on some facts given in this paper, we construct a new duality pair. Also, the Cartan–Eilenberg Gorenstein dimension of complexes is discussed.</p>

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Cartan–Eilenberg Gorenstein Complexes with Respect to Duality Pairs

  • 期刊论文

  • 发表日期：

    2026年5月20日

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  • Sixin Zhao,
  • Bo Lu

摘要

In this paper, we consider Cartan–Eilenberg Gorenstein complexes with respect to duality pairs. Using the properties of duality pairs, we investigate Cartan–Eilenberg Gorenstein complexes. Moreover, we establish a relationship between Cartan–Eilenberg Gorenstein \((\mathscr{X}, \, \mathscr{Y})\) -complexes and their terms for a duality pair \((\mathscr{X}, \, \mathscr{Y})\) of modules. Based on some facts given in this paper, we construct a new duality pair. Also, the Cartan–Eilenberg Gorenstein dimension of complexes is discussed.