Work

On the asymptotic Makar-Limanov rank conjecture

Year: 2026

Type: preprint

Abstract: Let $\Bbbk$ be an algebraically closed field of characteristic zero and let $f$ be a nonconstant polynomial in finitely many freely noncommuting variables. We prove the asymptotic Makar-Limanov rank conjecture, namely that the normalized rank of a value of $f$ can be made arbitrarily small by choosing matrices over $\Bbbk$ of finite size.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.06800

Authors: Yan, SiZhuo, Shen, Hao, Yang, Jianting

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Electronic Science and Technology of China

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220728840

Cites: 6

Cited by:

Related to: 10