从多项式环的理想成员问题到元胞群的 Dehn 函数

Wenhao Wang
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引用次数: 0

摘要

理想成员问题询问环中的元素是否属于给定的理想。在本文中,我们提出了一个反映具有整数系数的劳伦多项式环中理想成员问题复杂性的函数。我们还把定义的复杂度函数与元胞群的 Dehn 函数联系起来,希望能构造出具有超指数 Dehn 函数的元胞群。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
From Ideal Membership Problem for polynomial rings to Dehn Functions of Metabelian Groups
The ideal membership problem asks whether an element in the ring belongs to the given ideal. In this paper, we propose a function that reflecting the complexity of the ideal membership problem in the ring of Laurent polynomials with integer coefficients. We also connect the complexity function we define to the Dehn function of a metabelian group, in the hope of constructing a metabelian group with superexponential Dehn function.
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