Abstract Let R be a commutative ring with identity. Denote by the set of all R-modules admitting a finite projective resolution consisting of finitely generated projective modules. Then the small finitistic dimension of R is defined as Cahen et al. posed an open problem as follows: Let R be a Prüfer ring. Is ? In this paper, we show that the answer to this problem is negative. In the process of solving the problem, we need to give module-theoretic characterizations of the ring of finite fractions. Moreover, we introduce the concepts of FT-flat modules and the global FT-flat dimension of a ring to give a Prüfer-like characterization of the domains R with

中文翻译：

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每个 Prüfer 环不具有至多一个小的有限维数

摘要 令 R 是一个具有身份的交换环。由所有 R 模的集合表示，该集合允许由有限生成的射影模组成的有限射影分辨率。然后将 R 的小有限维定义为 Cahen 等人。提出了一个开放的问题如下：让 R 是一个 Prüfer 环。是 ？在本文中，我们表明这个问题的答案是否定的。在求解问题的过程中，我们需要给出有限分数环的模理论表征。此外，我们引入了 FT-flat 模块的概念和环的全局 FT-flat 维度，以给出域 R 的类似 Prüfer 的表征