Work

On a Rank Nullstellensatz Conjecture for Noncommutative Polynomials

Year: 2026

Type: preprint

Abstract: Jurij Volčič conjectured that a noncommutative polynomial $g$ belongs to the two-sided ideal generated by $f_1,\ldots,f_l$ if and only if, for matrices of every size, the rank of the evaluation of $g$ is bounded by a constant times the maximum rank of the evaluations of $f_1,\ldots,f_l$. In this paper, we show this equivalence when the generators $f_1,\ldots,f_l$ are homogeneous. We then give an explicit counterexample in the non-homogeneous case.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.01804

Authors: Yan, Sizhuo, Yang, Jianting

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

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7216086140

Cites: 1

Cited by: 1

Related to: 10