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arXiv · 2609.32152

The finite basis problem for additively idempotent semirings of order four, IV

Miaomiao Ren·Mengya Yue·Mengyu Yuan·Simin Lyu·Chenyu Yang·Ting Yu
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Abstract

This paper is the fourth in a series devoted to the finite basis problem for $4$-element additively idempotent semirings. These algebras are divided into five types according to their additive reducts; we study the largest of these types, namely those whose additive reducts are chains. Up to isomorphism, there are $386$ such algebras, denoted by $S_{(4, k)}$, $481 \leq k \leq 866$. We show that all but three of them, namely $S_{(4,545)}$, $S_{(4,634)}$, and $S_{(4,710)}$, are finitely based. This completes the classification, with respect to the finite basis property, of all $4$-element additively idempotent semirings with chain additive reducts.

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Miaomiao Ren, Mengya Yue, Mengyu Yuan, Simin Lyu, Chenyu Yang, Ting Yu. 2026-09-26. The finite basis problem for additively idempotent semirings of order four, IV. https://arxiv.org/abs/2609.32152

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