From Ideal Membership Problem for polynomial rings to Dehn Functions of Metabelian Groups

2024/08/02 by Wenhao Wang, Wang, Wenhao
Mathematics · #Advanced Algebra and Geometry #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2408.01518

openalex publication_date 2024/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• On the Dehn functions of a class of monadic one-relation monoids
• Ideal Membership in Polynomial Rings over the Integers
• Subgroup Distortion and the Relative Dehn Functions of Metabelian Groups
• On the effective membership problem for polynomial ideals
• Asymptotic invariants, complexity of groups and related problems