On the injectivity of evaluation maps induced by polynomials on certain algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911119628566528 |
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| author | Kutzschebauch, Frank Son, Tran Nam Vin, Pham Duy |
| author_facet | Kutzschebauch, Frank Son, Tran Nam Vin, Pham Duy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the injectivity of evaluation maps induced by polynomials on certain algebras Kutzschebauch, Frank Son, Tran Nam Vin, Pham Duy Rings and Algebras 15A24 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. |
| title | On the injectivity of evaluation maps induced by polynomials on certain algebras |
| topic | Rings and Algebras 15A24 |
| url | https://arxiv.org/abs/2508.17570 |