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 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}
}