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On a theorem by de Felipe and Teissier about the comparison of two henselisations in the non-noetherian case
Journal of Algebra ( IF 0.9 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.jalgebra.2020.11.020
María Emilia Alonso García , Henri Lombardi , Stefan Neuwirth

Let R be a local domain, $v$ a valuation of its quotient field centered in R at its maximal ideal. We investigate the relationship between R$^h$, the henselisation of R as local ring, and $\tilde{v}$, the henselisation of the valuation $v$, by focussing on the recent result by de Felipe and Teissier referred to in the title. We give a new proof that simplifies the original one by using purely algebraic arguments. This proof is moreover constructive in the sense of Bishop and previous work of the authors, and allows us to obtain as a by-product a (slight) generalization of the theorem by de Felipe and Teissier.

中文翻译:

关于 de Felipe 和 Teissier 的定理,关于非诺特情况下的两个 henselisation 的比较

设 R 是一个局部域,$v$ 是其最大理想下以 R 为中心的商域的估值。我们通过关注 de Felipe 和 Teissier 最近的结果,研究了 R$^h$(R 作为局部环的 henselisation)与 $\tilde{v}$(估值 $v$ 的 henselisation)之间的关系在标题中。我们给出了一个新的证明,通过使用纯代数论证来简化原始证明。此外,这个证明在 Bishop 和作者以前的工作的意义上是建设性的,并允许我们作为副产品获得 de Felipe 和 Teissier 定理的(轻微)推广。
更新日期:2021-03-01
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