论文标题
广义花样模块的决定性条件
Determinantal Conditions for Modules of Generalized Splines
论文作者
论文摘要
图形$ g $上的通用花键在通勤环$ r $中带有边缘标签是顶点标签，因此，如果两个顶点在$ g $中共享边缘，则顶点标签之间的差异在于边缘标签产生的理想。当$ r $是一个积分域时，所有此类花样的集合是有限生成的$ r $ r $ -module $ r_g等级$ n $，是$ g $的顶点的数量。我们在$ r_g $的子集上找到确定的确定条件，这些条件确定$ r_g $是否为免费模块，如果是的，是否存在所谓的“流动类基础”。
Generalized splines on a graph $G$ with edge labels in a commutative ring $R$ are vertex labelings such that if two vertices share an edge in $G$, the difference between the vertex labels lies in the ideal generated by the edge label. When $R$ is an integral domain, the set of all such splines is a finitely generated $R$-module $R_G$ of rank $n$, the number of vertices of $G$. We find determinantal conditions on subsets of $R_G$ that determine whether $R_G$ is a free module, and if so, whether a so called "flow-up class basis" exists.
