Over a commutative noetherian ring $R$ of finite Krull dimension, we show that every complex of flat cotorsion $R$-modules decomposes as a direct sum of a minimal complex and a contractible complex. Moreover, we define the notion of a semi-flat-cotorsion complex as a special type of semi-flat complex, and provide functorial ways to construct a quasi-isomorphism from a semi-flat complex to a semi-flat-cotorsion complex. Consequently, every $R$-complex can be replaced by a minimal semi-flat-cotorsion complex in the derived category over $R$. Furthermore, we describe structure of semi-flat-cotorsion replacements, by which we recover classic theorems for finitistic dimensions. In addition, we improve some results on cosupport and give a cautionary example. We also explain that semi-flat-cotorsion replacements always exist and can be used to describe the derived category over any associative ring.

中文翻译：

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最小的半扁平扭转替换和协同支撑

在有限 Krull 维的交换 noetherian 环 $R$ 上，我们证明了每个扁平 cotorsion $R$-模的复形分解为最小复形和可收缩复形的直接和。此外，我们将半平复形的概念定义为一种特殊类型的半平复形，并提供了构造从半平复形到半平复形的拟同构的函式方法。因此，每个 $R$-复形都可以被 $R$ 上的派生类别中的最小半平复形替代。此外，我们描述了半平坦扭曲替换的结构，通过它我们恢复了有限维数的经典定理。此外，我们改进了 cosupport 上的一些结果并给出了一个警示示例。