The finite basis problem for flat semirings S_c(W), M_c(W) and M(W)

@misc{gao2026finite,
  title = {{The finite basis problem for flat semirings $S_c(W)$, $M_c(W)$ and $M(W)$}},
  author = {Zidong Gao and Miaomiao Ren and Yilin Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.40155},
  eprint = {2609.40155},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.40155},
}

TY  - UNPB
TI  - The finite basis problem for flat semirings S_c(W), M_c(W) and M(W)
AU  - Zidong Gao
AU  - Miaomiao Ren
AU  - Yilin Zhou
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.40155
UR  - https://arxiv.org/abs/2609.40155
AB  - We study the finite basis problem for flat semirings of the forms S_c(W), M_c(W), and M(W), where W is a nonempty set of words in a free commutative semigroup, a free commutative monoid, and a free monoid, respectively. We completely classify such flat semirings with respect to the finite basis property, allowing W to be infinite. We prove that S_c(W) is finitely based if and only if every word in W is either a cube of a letter or has length at most two, whereas M_c(W) and M(W) are finitely based if and only if W consists solely of the empty word. As applications, we recover the nonfinite basability of ♭(ℤ) and the max-plus semiring (ℤ,max,+).
ER  -