Let R be a Mori domain with complete integral closure $\widehat R$, nonzero conductor $\mathfrak f = (R: \widehat R)$, and suppose that both v-class groups ${{\cal C}_v}(R)$ and ${{\cal C}_v}(3\widehat R)$ are finite. If $R \mathfrak f$ is finite, then the elasticity of R is either rational or infinite. If $R \mathfrak f$ is artinian, then unions of sets of lengths of R are almost arithmetical progressions with the same difference and global bound. We derive our results in the setting of v-noetherian monoids.

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关于 Mori Monoids 和域的算术

让R是完全积分闭包的 Mori 域$\宽帽R$, 非零导体$\mathfrak f = (R: \widehat R)$，并假设两者v- 阶级团体${{\cal C}_v}(R)$和${{\cal C}_v}(3\widehat R)$是有限的。如果$R \mathfrak f$是有限的，那么弹性R要么是有理的，要么是无限的。如果$R \mathfrak f$是 artinian，然后是长度集的并集R几乎是具有相同差异和全局界限的算术级数。我们在以下设置中得出我们的结果v- 诺特类幺半群。