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arXiv · 1608.05835

On flat epimorphisms of rings and pointwise localizations

Abolfazl Tarizadeh
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Abstract

In this paper all rings are commutative. We prove some new results on flat epimorphisms of rings and pointwise localizations. Especially among them, it is proved that a ring $R$ is an absolutely flat (von-Neumann regular) ring if and only if it is isomorphic to the pointwise localization $R^{(-1)}R$, or equivalently, each $R-$algebra is $R-$flat. For a given minimal prime ideal $\mathfrak{p}$ of a ring $R$, the surjectivity of the canonical map $R\rightarrow R_{\mathfrak{p}}$ is characterized. Finally, we give a new proof to the fact that in a flat epimorphism of rings, the contraction-extension of an ideal equals the same ideal.

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Abolfazl Tarizadeh. 2016-08-20. On flat epimorphisms of rings and pointwise localizations. https://arxiv.org/abs/1608.05835

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