Analytically unramified one-dimensional semilocal rings and their value semigroups
Analytically unramified one-dimensional semilocal rings and their value semigroups
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解析无枝一维半局部环及其值半群
DOI：
10.1016/s0022-4049(98)00160-1
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
R. Fröberg
中科院分区：
文献类型：
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作者：
V. Barucci;M. D'anna;R. Fröberg
在具有有限积分闭包的一维局部环R中，每个非零因子在Nd中有一个值，其中d是积分闭包中最大理想的个数。值的集合构成一个半群，即r的值半群。我们研究了值半群与环之间的联系。对于某些类型的环，如Gorenstein环、Arf环和小重环，存在着特别紧密的联系。在许多方面，阿尔夫圈和戈伦斯坦圈是截然相反的两个极端。给出了Lipman研究的爆破序列中的上环、交数和多重序列的应用。
In a one-dimensional local ring R with finite integral closure each nonzerodivisor has a value in Nd, where d is the number of maximal ideals in the integral closure. The set of values constitutes a semigroup, the value semigroup of R. We investigate the connection between the value semigroup and the ring. There is a particularly close connection for some classes of rings, e.g. Gorenstein rings, Arf rings, and rings of small multiplicity. In many respects, the Arf rings and the Gorenstein rings turn out to be opposite extremes. We give applications to overrings, intersection numbers, and multiplicity sequences in the blow-up sequences studied by Lipman.