# 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} }

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

#### One Citation

A characterisation of enveloping 1-tilting classes over commutative rings

- Mathematics

Abstract Given a 1-tilting cotorsion pair over a commutative ring , we characterise the rings over which the 1-tilting class is an enveloping class. To do so, we consider the faithful finitely… Expand

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