整环类的倒数补
The reciprocal complements of classes of integral domains
AI总结：
该研究围绕整环的倒数补$R(D)$展开，探究其素理想、局部化与Krull维数等性质，刻画多类整环的倒数补并给出$R(D)$为DVR的判定条件。
摘要：
给定整环$D$及其商域$\u200b\mathcal{Q}(D)$，$D$的倒数补是$\u200b\mathcal{Q}(D)$的子环$R(D)$，其元素为$D$中所有非零元$d_1,\ldots,d_n$对应的和$\frac{1}{d_1}+\ldots+\frac{1}{d_n}$。本文研究了$R(D)$型环的素理想、局部化与Krull维数相关问题，刻画了包括半群代数、$D+\mathfrak{m}$构造在内的几类整环的倒数补，还给出了$R(D)$为离散赋值环（DVR）的判定条件。
英文摘要：
Given an integral domain $D$ with quotient field $\mathcal{Q}(D)$, the reciprocal complement of $D$ is the subring $R(D)$ of $\mathcal{Q}(D)$ whose elements are all the sums $\frac{1}{d_1}+\ldots+\frac{1}{d_n} $ for $d_1, \ldots, d_n$ nonzero elements of $D$. In this article we study problems related with prime ideals, localizations and Krull dimension of rings of the form $R(D)$ and we describe the reciprocal complements of classes of domains, including semigroup algebras and $ D+ \mathfrak{m} $ constructions. We also characterize when $R(D)$ is a DVR.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
