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arXiv · 2610.21605

Two-element factors and finite bases for additively idempotent semirings

Qirui Ma·Mengya Yue
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Abstract

For every additively idempotent semiring $S$ in the constant-free signature, $S$ is finitely based if and only if $S\times E$ is finitely based when $E=M_2$ or $T_2$. For each $E\in\{L_2,R_2,D_2,N_2\}$, both implications fail even for finite $S$: we give a finite finitely based semiring whose product with $E$ is nonfinitely based and a finite nonfinitely based semiring whose product with $E$ is finitely based.

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Qirui Ma, Mengya Yue. 2026-10-17. Two-element factors and finite bases for additively idempotent semirings. https://arxiv.org/abs/2610.21605

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