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

@misc{ren2026finite,
  title = {{The finite basis problem for additively idempotent semirings of order four, IV}},
  author = {Miaomiao Ren and Mengya Yue and Mengyu Yuan and Simin Lyu and Chenyu Yang and Ting Yu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32152},
  eprint = {2609.32152},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32152},
}

TY  - UNPB
TI  - The finite basis problem for additively idempotent semirings of order four, IV
AU  - Miaomiao Ren
AU  - Mengya Yue
AU  - Mengyu Yuan
AU  - Simin Lyu
AU  - Chenyu Yang
AU  - Ting Yu
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32152
UR  - https://arxiv.org/abs/2609.32152
AB  - 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 ≤ k ≤ 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.
ER  -