基于不变量$(c-δ)r-δ$的一维局部域分类
A classification of one-dimensional local domains based on the invariant $(c-δ)r-δ$
摘要：
设$R$是一维局部Noether整环，$\R$是$R$在其商域上的积分闭包，$v(R)$是由通常赋值定义的值集.研究了非负不变量$b:=(c-δ)r- δ$，其中$c, δ, r$分别表示导体、$\R/R$的长度和Cohen Macaulay型.特别地，实现了具有$b\leq 2(r-1)$的环的半群$v(R)$的分类。这种分类方法可以成功地利用类似的论点，但更无聊的计算情况下，$b\leq q(r-1), $的$q$值合理较低。主要工具是类型序列和不变$k$，它估计$v(R)$中属于区间$[c-e,c), e$的元素的数量，该区间是$R$的重数。
英文摘要：
Let $R$ be a one-dimensional, local, Noetherian domain, $\R$ the integral closure of $R$ in its quotient field and $v(R)$ the value set defined by the usual valuation. The aim of the paper is to study the non-negative invariant $b:=(c-δ)r- δ$, where $c, δ, r$ denote the conductor, the length of $\R/R$ and the Cohen Macaulay type, respectively. In particular, the classification of the semigroups $v(R)$ for rings having $b\leq 2(r-1)$ is realized. This method of classification might be successfully utilized with similar arguments but more boring computations in the cases $b\leq q(r-1), $ for reasonably low values of $q$. The main tools are type sequences and the invariant $k$ which estimates the number of elements in $v(R)$ belonging to the interval $[c-e,c), e$ being the multiplicity of $R$.
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