On the injectivity of evaluation maps induced by polynomials on certain algebras
Rings and Algebras
2025-08-26 v1
Abstract
We explore the injectivity of the evaluation map eva f,A from Am A to A, where A is an associative algebra over a field F, and f is a polynomial in m \ge 1 variables with coefficients in F. Our investigation reveals that injectivity is possible only when m equal 1 and f has degree one; for functions in two or more variables, such injectivity is impossible.
Cite
@article{arxiv.2508.17570,
title = {On the injectivity of evaluation maps induced by polynomials on certain algebras},
author = {Frank Kutzschebauch and Tran Nam Son and Pham Duy Vin},
journal= {arXiv preprint arXiv:2508.17570},
year = {2025}
}