On the injectivity of evaluation maps induced by polynomials on certain algebras

2025/08/25 by Kutzschebauch, Frank, Son, Tran Nam, Vin, Pham Duy
#15A24 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.17570

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 ≥ 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.

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