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arXiv · 2604.13916

Commutativity of centralizers in a coproduct of a free algebra and a polynomial algebra

Jakob Jurij Snoj
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Abstract

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.

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Jakob Jurij Snoj. 2026-04-15. Commutativity of centralizers in a coproduct of a free algebra and a polynomial algebra. https://arxiv.org/abs/2604.13916

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