Characterizing diophantine henselian valuation rings and valuation ideals CHARACTERIZING DIOPHANTINE HENSELIAN VALUATION RINGS
Characterizing diophantine henselian valuation rings and valuation ideals CHARACTERIZING DIOPHANTINE HENSELIAN VALUATION RINGS
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丢番图亨塞尔估值环的特征和估值理想 丢番图亨塞尔估值环的特征
DOI：
10.1112/plms.12042
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发表时间：
2017
影响因子：
1.8
通讯作者：
Anscombe S
中科院分区：
文献类型：
--
作者：
Anscombe S
我们根据残差场，对这些汉塞尔估价环和那些丢番图的汉塞尔估价理想进行了表征。这种表征给出了文献中关于丢番图亨塞尔估值环和丢番图估值理想的所有正面和负面结果的共同概括。我们还处理一致性问题，并应用结果来表明给定域最多可以携带一个丢番图非平凡等特征亨塞尔估值环或估值理想。
We give a characterization, in terms of the residue field, of those henselian valuation rings and those henselian valuation ideals that are diophantine. This characterization gives a common generalization of all the positive and negative results on diophantine henselian valuation rings and diophantine valuation ideals in the literature. We also treat questions of uniformity and we apply the results to show that a given field can carry at most one diophantine nontrivial equicharacteristic henselian valuation ring or valuation ideal.