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Search: authors:"Gabriel Picavet"

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Pointwise minimal extensions

We characterize pointwise minimal extensions of rings, introduced by Cahen et al. (Rocky Mt J Math 41:1081–1125, 2011), in the special context of domains. We show that pointwise minimal extensions are either integral or integrally closed. In the closed case, they are nothing but minimal extensions. Otherwise, there are four cases: either all minimal sub-extensions are of the same...

Ascending the divided and going-down properties by absolute flatness

This paper aims to show that the “going-down ring” and the “divided ring” properties ascend along flat morphisms whose co-diagonal morphisms are flat, the so-called absolutely flat morphisms introduced by Olivier. But unibranchedness hypotheses are necessary as any henselization morphism shows. As a by-product, we get that the “unibranched divided ring” property is preserved by...