Valuation semigroups of two‐dimensional local rings
Valuation semigroups of two‐dimensional local rings
复制标题
二维局部环的估价半群
DOI：
10.1112/plms/pdt023
复制
发表时间：
2011
影响因子：
1.8
通讯作者：
Pham An Vinh
中科院分区：
文献类型：
--
作者：
S. Cutkosky;Pham An Vinh
我们考虑了一个半群何时是一个赋值支配一个二维诺特域的半群的问题，给出了一些令人惊讶的例子。给出了半群S与域扩张L/？是半群和剩余域的一个赋值控制一个具有剩余域？的2维正则局部环R，推广Spivakovsky定理的情况下，没有剩余域扩张。
We consider the question of when a semigroup is the semigroup of a valuation dominating a two‐dimensional noetherian domain, giving some surprising examples. We give a necessary and sufficient condition for the pair of a semigroup S and a field extension L/? to be the semigroup and residue field of a valuation dominating a regular local ring R of dimension 2 with residue field ?, generalizing the theorem of Spivakovsky for the case when there is no residue field extension.