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arXiv · 2512.23839

Prime ideals in the Boolean polynomial semiring

Kalina Mincheva·Naufil Sakran
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Abstract

In this article, we disprove a conjecture of F. Alarcón and D. Anderson and give a complete classification of the prime ideals in the one variable polynomial semiring with coefficients in Boolean semifield. We group the prime ideals of $\mathbb{B}[x]$ into three classes, indexed by integers.

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Kalina Mincheva, Naufil Sakran. 2026-04-15. Prime ideals in the Boolean polynomial semiring. https://arxiv.org/abs/2512.23839

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