Let ℰ be an injectively resolving subcategory of left R-modules. We introduce and study ℰ-Gorenstein flat modules as a common generalization of some known modules such as Gorenstein flat modules (Enochs, Jenda and Torrecillas, 1993), Gorenstein AC-flat modules (Bravo, Estrada and Iacob, 2018). Then we define a resolution dimension relative to the ℰ-Gorensteinflat modules, investigate the properties of the homological dimension and unify some important properties possessed by some known homological dimensions. In addition, stability of the category of ℰ-Gorensteinflat modules is discussed, and some known results are obtained as applications.

中文翻译：

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与内射解析子类别相关的 Gorenstein 平面模块

让ℰ是 left 的一个单射解析子类别R-模块。介绍研究ℰ-Gorenstein 扁平模块作为一些已知模块的常见概括，例如 Gorenstein 扁平模块（Enochs、Jenda 和 Torrecillas，1993 年）、Gorenstein AC 扁平模块（Bravo、Estrada 和 Iacob，2018 年）。然后我们定义一个相对于ℰ-Gorensteinflat模块，研究同调维的性质，统一一些已知同调维所具有的一些重要性质。此外，类别的稳定性ℰ-讨论了Gorensteinflat模块，并获得了一些已知结果作为应用程序。