Year: 2026
Type: preprint
Abstract: We prove that the three-element flat semiring $S_7$ is strongly nonfinitely based within the class of additively idempotent semirings. More generally, let $\mathcal N$ be the subvariety of $\Var(S_7)$ defined by $x^2y\approx x^2$. For every finite ai-semiring $A$, each variety $\mathcal W$ satisfying $\mathcal N\subseteq\mathcal W\subseteq\Var(A)$ has infinite axiomatic rank.
Source: arXiv (Cornell University)
Authors: Yue, Mengya, Shao, Xiaolei
Institution: Northwest University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221836282