arXiv 0801.04492008-01-02math.ACmath.AG

控制局部区域的赋值半群

Semigroups of valuations dominating local domains

Steven Dale Cutkosky

摘要：

给出了半群是等特征局部整环上的赋值控制半群的一个新的判别准则。该准则被用来构造正有理数的有序子半群的例子，这些子半群是有序型Ω，但不是等特征Noether局部域上赋值的值半群。这表明Zenski和Samuel的书“交换代数”的附录3中给出的关于值半群的必要条件是不充分的。

英文摘要：

A new criterion is given for a semigroup to be the semigroup of a valuation dominating an equicharacteristic local domain. The criterion is used to construct examples of well ordered subsemigroups of the positive rational numbers which are of ordinal type omega, but are not the value semigroup of a valuation on an equicharacteristic noetherian local domain. This shows that the necessary conditions on value semigroups given in Appendix 3 to Zariski and Samuel's book ``Commutative Algebra'' are not sufficient.

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