{"language":[{"iso":"eng"}],"_id":"58187","user_id":"102487","doi":"10.1007/s13366-025-00800-2","author":[{"id":"102487","last_name":"Seguin","first_name":"Beranger Fabrice","full_name":"Seguin, Beranger Fabrice"}],"title":"Symmetries of various sets of polynomials","status":"public","year":"2025","date_updated":"2025-07-16T13:51:54Z","date_created":"2025-01-15T11:25:18Z","external_id":{"arxiv":["2407.09118"]},"type":"journal_article","citation":{"ieee":"B. F. Seguin, “Symmetries of various sets of polynomials,” <i>Beiträge zur Algebra und Geometrie</i>, 2025, doi: <a href=\"https://doi.org/10.1007/s13366-025-00800-2\">10.1007/s13366-025-00800-2</a>.","apa":"Seguin, B. F. (2025). Symmetries of various sets of polynomials. <i>Beiträge Zur Algebra Und Geometrie</i>. <a href=\"https://doi.org/10.1007/s13366-025-00800-2\">https://doi.org/10.1007/s13366-025-00800-2</a>","chicago":"Seguin, Beranger Fabrice. “Symmetries of Various Sets of Polynomials.” <i>Beiträge Zur Algebra Und Geometrie</i>, 2025. <a href=\"https://doi.org/10.1007/s13366-025-00800-2\">https://doi.org/10.1007/s13366-025-00800-2</a>.","short":"B.F. Seguin, Beiträge Zur Algebra Und Geometrie (2025).","mla":"Seguin, Beranger Fabrice. “Symmetries of Various Sets of Polynomials.” <i>Beiträge Zur Algebra Und Geometrie</i>, 2025, doi:<a href=\"https://doi.org/10.1007/s13366-025-00800-2\">10.1007/s13366-025-00800-2</a>.","bibtex":"@article{Seguin_2025, title={Symmetries of various sets of polynomials}, DOI={<a href=\"https://doi.org/10.1007/s13366-025-00800-2\">10.1007/s13366-025-00800-2</a>}, journal={Beiträge zur Algebra und Geometrie}, author={Seguin, Beranger Fabrice}, year={2025} }","ama":"Seguin BF. Symmetries of various sets of polynomials. <i>Beiträge zur Algebra und Geometrie</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1007/s13366-025-00800-2\">10.1007/s13366-025-00800-2</a>"},"publication":"Beiträge zur Algebra und Geometrie","abstract":[{"text":"Let $K$ be a field of characteristic $0$ and $k \\geq 2$ be an integer. We\r\nprove that every $K$-linear bijection $f : K[X] \\to K[X]$ strongly preserving\r\nthe set of $k$-free polynomials (or the set of polynomials with a $k$-fold root\r\nin $K$) is a constant multiple of a $K$-algebra automorphism of $K[X]$, i.e.,\r\nthere are elements $a, c \\in K^{\\times}$, $b \\in K$ such that $f(P)(X) = c P(a\r\nX + b)$. When $K$ is a number field or $K=\\mathbb{R}$, we prove that similar\r\nstatements hold when $f$ preserves the set of polynomials with a root in $K$.","lang":"eng"}]}