论文标题
DP最小积分域
Dp-minimal integral domains
论文作者
论文摘要
结果表明，每个DP-Minimal积分域$ r $都是本地戒指，对于$ r $ $ r $的每个非最大值的prime $ \ mathfrak p $ p $ $ r $，本地化$ r _ {\ mathfrak p} $是一个估值环，$ \ \ \ \ m m mathfrak {p} r _ {\ mathfrak {\ mathfrak {\ mathfrak}此外，当且仅当其残基领域是无限的或其残留场是有限的，并且其最大理想是主要的，DP最小整体域是一个估值环。
It is shown that every dp-minimal integral domain $R$ is a local ring and for every non-maximal prime ideal $\mathfrak p $ of $R$, the localization $R_{\mathfrak p }$ is a valuation ring and $\mathfrak{p}R_{\mathfrak{p}}=\mathfrak{p}$. Furthermore, a dp-minimal integral domain is a valuation ring if and only if its residue field is infinite or its residue field is finite and its maximal ideal is principal.
