论文标题
半群环是微弱的krull域
Semigroup rings as weakly Krull domains
论文作者
论文摘要
令$ d $是一个积分域，$γ$是具有身份元素和商组$ g $的无扭转的可交换（添加剂）半群。 In this paper, we show that if char$(D)=0$ (resp., char$(D)=p>0$), then $D[Γ]$ is a weakly Krull domain if and only if $D$ is a weakly Krull UMT-domain, $Γ$ is a weakly Krull UMT-monoid, and $G$ is of type $(0,0,0, \dots )$ (resp., type $(0,0,0, \ dots）$除$ p $）。此外，我们给出了此结果的算术应用。
Let $D$ be an integral domain and $Γ$ be a torsion-free commutative cancellative (additive) semigroup with identity element and quotient group $G$. In this paper, we show that if char$(D)=0$ (resp., char$(D)=p>0$), then $D[Γ]$ is a weakly Krull domain if and only if $D$ is a weakly Krull UMT-domain, $Γ$ is a weakly Krull UMT-monoid, and $G$ is of type $(0,0,0, \dots )$ (resp., type $(0,0,0, \dots )$ except $p$). Moreover, we give arithmetical applications of this result.
