English

Prime ideals in the Boolean polynomial semiring

Commutative Algebra 2026-04-16 v2 Rings and Algebras

Abstract

In this article, we disprove a conjecture of F. Alarc\'on 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 B[x]\mathbb{B}[x] into three classes, indexed by integers.

Keywords

Cite

@article{arxiv.2512.23839,
  title  = {Prime ideals in the Boolean polynomial semiring},
  author = {Kalina Mincheva and Naufil Sakran},
  journal= {arXiv preprint arXiv:2512.23839},
  year   = {2026}
}
R2 v1 2026-07-01T08:45:02.448Z