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The six-element additively idempotent semiring B21 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 B21 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 B21.

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Cite

BibTeXRIS
BibTeX
@misc{ren2026sixelement,
  title = {{The six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based}},
  author = {Miao Miao Ren and Meng Ya Yue and Yi Lin Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12491},
  eprint = {2610.12491},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12491},
}
RIS
TY  - UNPB
TI  - The six-element additively idempotent semiring B_2^1 is inherently nonfinitely based
AU  - Miao Miao Ren
AU  - Meng Ya Yue
AU  - Yi Lin Zhou
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.12491
UR  - https://arxiv.org/abs/2610.12491
AB  - 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.
ER  -