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FCP $$\Delta $$ Δ -extensions of rings
Arabian Journal of Mathematics Pub Date : 2020-11-02 , DOI: 10.1007/s40065-020-00298-7
Gabriel Picavet , Martine Picavet-L’Hermitte

We consider ring extensions, whose set of all subextensions is stable under the formation of sums, the so-called \(\Delta \)-extensions. An integrally closed extension has the \(\Delta \)-property if and only it is a Prüfer extension. We then give characterizations of FCP \(\Delta \)-extensions, using the fact that for FCP extensions, it is enough to consider integral FCP extensions. We are able to give substantial results. In particular, our work can be applied to extensions of number field orders because they have the FCP property.



中文翻译:

FCP $$ \ Delta $$Δ-环的延伸

我们考虑环扩展,它的所有子扩展的集合在和的形成下都是稳定的,即所谓的\(\ Delta \)-扩展。当且仅当是Prüfer扩展时,一个整体封闭的扩展才具有\(\ Delta \)属性。然后,我们使用FCP扩展就足以考虑整体FCP扩展的事实,给出FCP \(\ Delta \)扩展的特征。我们能够给出实质性的结果。特别是,我们的工作可以应用于数字现场订单的扩展,因为它们具有FCP属性。

更新日期:2020-11-02
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