Preserving zeros of a polynomial

TL;DR

This paper investigates mappings on matrix subsets that preserve the zeros of specific noncommutative polynomials, contributing to the understanding of structure-preserving transformations in matrix algebra.

Contribution

It introduces a framework for analyzing zero-preserving maps related to multilinear polynomials in noncommuting variables.

Findings

Characterization of zero-preserving mappings on matrix subsets.

Identification of conditions under which such mappings are structure-preserving.

Extension of classical preservers to noncommutative polynomial zeros.

Abstract

We study non-linear surjective mappings on subsets of ${\cal M}_n(F)$, which preserve the zeros of some fixed polynomials in noncommuting variables. Keywords: Matrix algebra, Multilinear polynomials, Preservers.