A nonfinitely based additively idempotent semiring of order four
Group Theory
2026-05-18 v1
Abstract
We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semirings satisfying this condition, including a -element semiring whose additive reduct has two minimal elements and two coatoms. Consequently, these semirings have no finite basis for their identities.
Cite
@article{arxiv.2605.15493,
title = {A nonfinitely based additively idempotent semiring of order four},
author = {Mengya Yue and Miaomiao Ren},
journal= {arXiv preprint arXiv:2605.15493},
year = {2026}
}