Abstract
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 the formation of factor domains and by localization with respect to prime ideals. Moreover, we exhibit some ascent results for the “going-down ring” and “divided ring” properties along integral extensions.
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Picavet, G. Ascending the divided and going-down properties by absolute flatness. Arab. J. Math. 1, 113–126 (2012). https://doi.org/10.1007/s40065-012-0008-3
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DOI: https://doi.org/10.1007/s40065-012-0008-3