关于de Felipe和Teissier关于非Noether情形下两个Henselisation比较的一个定理
On a theorem by de Felipe and Teissier about the comparison of two henselisations in the non-noetherian case
摘要：
设R是局部整环，v是以R为中心的商域在其极大理想上的赋值.本文研究了R作为局部环的Henselisation（R^h）与赋值v的Henselisation（{v}）之间的关系，并着重讨论了标题中提到的de Felipe和Teissier的最新结果.我们给出了一个新的证明，简化了原来的一个使用纯代数参数。这个证明是建设性的意义上的主教和以前的工作的作者，并允许我们获得作为一个副产品的（轻微）概括定理的费利佩和Teissier。
英文摘要：
Let R be a local domain, v a valuation of its quotient field centred in R at its maximal ideal. We investigate the relationship between R^h, the henselisation of R as local ring, and {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) generalisation of the theorem by de Felipe and Teissier.
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