格理想的边基
Border bases for lattice ideals
摘要：
构造理想I $\subseteq$ K[x 1，. .., xn]是阶理想O，其是K-向量空间K[x1，.. .., [xn]在本文中，我们给出了一个程序，以找到所有可能的阶理想与一个格理想IM（其中M是一个格Z n）。该结构可以应用于任何维数的理想（不仅是零维），并表明可能的阶理想总是有限的。对于正维数的格理想，我们还表明，虽然边界基是无限的，它可以被定义在有限项。此外，我们给出了一个例子，证明了不是所有的格理想的边界基来自Gröbner基地。最后，我们给出了一个完整的和明确的描述所有的边界基地的理想IM的情况下M是一个2维格包含在Z 2。
英文摘要：
The main ingredient to construct an O-border basis of an ideal I $\subseteq$ K[x1,. .., xn] is the order ideal O, which is a basis of the K-vector space K[x1,. .., xn]/I. In this paper we give a procedure to find all the possible order ideals associated with a lattice ideal IM (where M is a lattice of Z n). The construction can be applied to ideals of any dimension (not only zero-dimensional) and shows that the possible order ideals are always in a finite number. For lattice ideals of positive dimension we also show that, although a border basis is infinite, it can be defined in finite terms. Furthermore we give an example which proves that not all border bases of a lattice ideal come from Gröbner bases. Finally, we give a complete and explicit description of all the border bases for ideals IM in case M is a 2-dimensional lattice contained in Z 2 .
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。
