Commutativity of centralizers in a coproduct of a free algebra and a polynomial algebra
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
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| _version_ | 1866911595711430656 |
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| author | Snoj, Jakob Jurij |
| author_facet | Snoj, Jakob Jurij |
| contents | We show that the centralizer of a nonscalar element in the coproduct $k\langle X\rangle *k[Y]$ of a free associative algebra and a polynomial algebra over a given field is commutative. For $k\langle X \rangle$ this is part of Bergman's centralizer theorem. Our proof relies on a reduction given in Bergman's proof and is of combinatorial nature, employing a strict order structure of the coproduct monoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13916 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Commutativity of centralizers in a coproduct of a free algebra and a polynomial algebra Snoj, Jakob Jurij Rings and Algebras We show that the centralizer of a nonscalar element in the coproduct $k\langle X\rangle *k[Y]$ of a free associative algebra and a polynomial algebra over a given field is commutative. For $k\langle X \rangle$ this is part of Bergman's centralizer theorem. Our proof relies on a reduction given in Bergman's proof and is of combinatorial nature, employing a strict order structure of the coproduct monoid. |
| title | Commutativity of centralizers in a coproduct of a free algebra and a polynomial algebra |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2604.13916 |