论文标题
交换环的矿石延伸和二摩根
Ore extensions of commutative rings and the Dixmier-Moeglin equivalence
论文作者
论文摘要
我们考虑表格$ t的矿石扩展：= r [x;σ，δ] $，$ r $一个可交换的积分域，该域是有限地生成在字段$ k $上的。我们表明，如果$ t $的gelfand-kirillov尺寸小于四个，那么{\ rm spec}（t）$ in {\ rm spec}（t）$的主要理想$ p \是原始的。我们还表明，有一些示例，这些等价并非全部适用于整数Gelfand-Kirillov尺寸，大于或等于$ 4 $。
We consider Ore extensions of the form $T:=R[x;σ,δ]$ with $R$ a commutative integral domain that is finitely generated over a field $k$. We show that if $T$ has Gelfand-Kirillov dimension less than four then a prime ideal $P\in {\rm Spec}(T)$ is primitive if and only if $\{P\}$ is locally closed in ${\rm Spec}(T)$, if and only if the Goldie ring of quotients of $T/P$ has centre that is an algebraic extension of $k$. We also show that there are examples for which these equivalences do not all hold for $T$ of integer Gelfand-Kirillov dimension greater than or equal to $4$.
