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<p>In this paper, we study the relationship of balanced pairs in a recollement. As an application of balanced pairs, we introduce the notion of the relative tilting objects, and give a characterization of relative tilting objects, which is similar to Bazzoni characterization of <i>n</i>-tilting modules. Finally, we investigate the relationship of relative tilting objects in a recollement.</p>

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Balanced Pairs and Relative Tilting Objects in Recollements of Abelian Categories

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Peiyu Zhang,
  • Menghui Liu,
  • Dajun Liu,
  • Jiaqun Wei

摘要

In this paper, we study the relationship of balanced pairs in a recollement. As an application of balanced pairs, we introduce the notion of the relative tilting objects, and give a characterization of relative tilting objects, which is similar to Bazzoni characterization of n-tilting modules. Finally, we investigate the relationship of relative tilting objects in a recollement.