Flat Commutative Ring Epimorphisms of Almost Krull Dimension Zero

@article{Positselski2021FlatCR,
  title={Flat Commutative Ring Epimorphisms of Almost Krull Dimension Zero},
  author={Leonid Positselski},
  journal={Journal of Algebra and Its Applications},
  year={2021}
}
  • L. Positselski
  • Published 7 September 2020
  • Mathematics
  • Journal of Algebra and Its Applications
We consider flat epimorphisms of commutative rings $R\to U$ such that, for every ideal $I\subset R$ for which $IU=U$, the quotient ring $R/I$ is semilocal of Krull dimension zero. Under these assumptions, we show that the projective dimension of the $R$-module $U$ does not exceed $1$. We also describe the Geigle-Lenzing perpendicular subcategory $U^{\perp_{0,1}}$ in $R\mathsf{-Mod}$. Assuming additionally that the ring $U$ and all the rings $R/I$ are perfect, we show that all flat $R$-modules… Expand
1 Citations
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