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arXiv · 2601.21209

Positive characteristic analogues of finite algebraic numbers

Daichi Matsuzuki·Honami Sakamoto·Jun Ueki
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Abstract

J.~Rosen introduced the ring $\mathcal{P}^0_{\mathcal{A}}$ of so-called finite algebraic numbers, which may be seen as an analogue of certain periods in the ring $\mathcal{A}=\prod_p \mathbb{Z}/p\mathbb{Z} /\bigoplus_p \mathbb{Z}/p\mathbb{Z}$, $p$ running through all prime numbers. In this article, we introduce its positive characteristic analogue $\mathcal{P}^0_{\mathcal{A}_K}$ over the rational function field $K=\mathbb{F}_q(\theta)$, $q$ being a prime power, and study foundational properties, and provide further scopes.

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Daichi Matsuzuki, Honami Sakamoto, Jun Ueki. 2026-01-29. Positive characteristic analogues of finite algebraic numbers. https://arxiv.org/abs/2601.21209

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