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arXiv · 2508.17570

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

Frank Kutzschebauch·Tran Nam Son·Pham Duy Vin
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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.

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Frank Kutzschebauch, Tran Nam Son, Pham Duy Vin. 2025-08-25. On the injectivity of evaluation maps induced by polynomials on certain algebras. https://arxiv.org/abs/2508.17570

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