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arXiv · 2610.12491

The six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based

Miao Miao Ren·Meng Ya Yue·Yi Lin Zhou
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Abstract

We show that the six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based. More precisely, for every positive integer $n$, we construct an infinite additively idempotent semiring, generated by at most $(6n+8)^2$ elements, that satisfies every $n$-variable identity of $B_2^1$.

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Miao Miao Ren, Meng Ya Yue, Yi Lin Zhou. 2026-09-22. The six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based. https://arxiv.org/abs/2610.12491

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