论文标题
一维赛车领域的恒星操作数量的渐近数
Asymptotic for the number of star operations on one-dimensional Noetherian domains
论文作者
论文摘要
我们研究了当地Noetherian域上的一组恒星操作，$ d $ dimension $ 1 $，以便导体$（d：t）$（其中$ t $是$ d $的整体关闭）等于$ d $的最大理想。我们将这个问题减少到有限扩展中的一类封闭操作（更精确的乘法操作）$ k \ subseteq b $中，其中$ k $是一个字段，然后我们研究这套关闭的基数如何变化，而$ k $的大小会有所不同，而$ b $的结构仍然固定。
We study the set of star operations on local Noetherian domains $D$ of dimension $1$ such that the conductor $(D:T)$ (where $T$ is the integral closure of $D$) is equal to the maximal ideal of $D$. We reduce this problem to the study of a class of closure operations (more precisely, multiplicative operations) in a finite extension $k\subseteq B$, where $k$ is a field, and then we study how the cardinality of this set of closures vary as the size of $k$ varies while the structure of $B$ remains fixed.
