摘要翻译:
给出了半群是赋值支配等分局部区域的半群的一个新判据。利用该判据构造了正有理数的有序子半群的例子,这些正有理数的序型为omega,但不是等元非以太局部区域上的值半群。这表明Zariski和Samuel在《交换代数》一书附录3中给出的关于值半群的必要条件是不充分的。
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英文标题:
《Semigroups of valuations dominating local domains》
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作者:
Steven Dale Cutkosky
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Commutative Algebra 交换代数
分类描述:Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环,模,理想,同调代数,计算方面,不变理论,与代数几何和组合学的联系
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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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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PDF链接:
https://arxiv.org/pdf/0801.0449