Let $R$ be a ring. We study the FG-pure exact sequences, which are defined analogously to pure exact sequences except with respect to finitely generated $R$-modules rather than the finitely presented $R$-modules. For Noetherian rings the two notions coincide. But for non-Noetherian rings, the FG-purity is sharper than the usual purity. We also study the corresponding notion of FG-flat module and construct a model for the FG-pure derived category. It is a compactly generated triangulated category.

中文翻译：

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FG-purity 和 FG-flat 模块

让R轴承。我们研究FG-纯精确序列，其定义类似于纯精确序列，除了有限生成R-模块而不是有限呈现的R-模块。对于诺特环来说，这两个概念是一致的。但对于非诺特环，FG 纯度比通常的纯度更清晰。我们还研究了相应的概念FG-扁平模块并为 FG-pure 派生类别构建模型。它是一个紧凑生成的三角分类。