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PreprintCC BY 4.0arXiv

Strong nonfinite basability of the three-element flat semiring S7

  • Mengya Yue
  • Xiaolei Shao
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Abstract

We prove that the three-element flat semiring S7 is strongly nonfinitely based within the class of additively idempotent semirings. More generally, let 𝒩 be the subvariety of Var(S7) defined by x2yβ‰ˆ x2. For every finite ai-semiring A, each variety 𝒲 satisfying π’©βŠ†π’²βŠ†Var(A) has infinite axiomatic rank.

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Cite

BibTeXRIS
BibTeX
@misc{yue2026strong,
  title = {{Strong nonfinite basability of the three-element flat semiring $S_7$}},
  author = {Mengya Yue and Xiaolei Shao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14068},
  eprint = {2610.14068},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14068},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Strong nonfinite basability of the three-element flat semiring S_7
AU  - Mengya Yue
AU  - Xiaolei Shao
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.14068
UR  - https://arxiv.org/abs/2610.14068
AB  - We prove that the three-element flat semiring S_7 is strongly nonfinitely based within the class of additively idempotent semirings. More generally, let 𝒩 be the subvariety of Var(S_7) defined by x^2yβ‰ˆ x^2. For every finite ai-semiring A, each variety 𝒲 satisfying π’©βŠ†π’²βŠ†Var(A) has infinite axiomatic rank.
ER  -