Scholarlink

<p>Let <i>Q</i> be a quiver and <i>R</i> an associative ring. A representation by <i>R</i>-modules of <i>Q</i> is called strongly fp-injective if it admits a pure acyclic injective resolution in the category of representations. It is shown that such representations possess many nice properties. We characterize strongly fp-injective representations under some mild assumptions, which is closely related to strongly fp-injective <i>R</i>-modules. Subsequently, we use such representations to define relative Gorenstein injective representations, called Gorenstein strongly fp-injective representations, and give an explicit characterization of the Gorenstein strongly fp-injective representations of certain right rooted quivers. As an application, a model structure in the category of representations is given.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Homological Theory of Representations Having Pure Acyclic Injective Resolutions

  • 期刊论文

  • 发表日期：

    2025年2月25日

查看全文
  • Qihui Li,
  • Junpeng Wang,
  • Gang Yang

摘要

Let Q be a quiver and R an associative ring. A representation by R-modules of Q is called strongly fp-injective if it admits a pure acyclic injective resolution in the category of representations. It is shown that such representations possess many nice properties. We characterize strongly fp-injective representations under some mild assumptions, which is closely related to strongly fp-injective R-modules. Subsequently, we use such representations to define relative Gorenstein injective representations, called Gorenstein strongly fp-injective representations, and give an explicit characterization of the Gorenstein strongly fp-injective representations of certain right rooted quivers. As an application, a model structure in the category of representations is given.