具有相同诱导序的不同单项序
Distinct monomial orders with same induced orderings
摘要：
本文证明了$R_n=K[X_1,...X_n]$中单项式的字典序、度字典序和度逆字典序是由它们的诱导序唯一确定的（即它们对$R_{n,i}=K[X_1,..., \hat{X_i}, .., X_n]$的限制），当$n \geq 4$ .我们还表明，对于任何$n \geq 4$有单项式的订单，不是唯一确定的诱导排序，并提供这些订单的例子为每个$n$。
英文摘要：
We prove that the lexicographic, degree lexicographic and the degree reverse lexicographic orders for monomials in $R_n=K[X_1,...X_n]$ are uniquely determined by their induced orderings, (i.e. their restrictions to $R_{n,i}=K[X_1,..., \hat{X_i}, .., X_n]$), when $n \geq 4$. We also show that for any $n \geq 4$ there are monomial orders that are not uniquely determined by their induced orderings, and provide examples of these orders for each $n$.
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。
