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PreprintarXiv licencearXiv

Two-element factors and finite bases for additively idempotent semirings

  • Qirui Ma
  • Mengya Yue
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Abstract

For every additively idempotent semiring S in the constant-free signature, S is finitely based if and only if S× E is finitely based when E=M2 or T2. For each E∈{L2,R2,D2,N2}, both implications fail even for finite S: we give a finite finitely based semiring whose product with E is nonfinitely based and a finite nonfinitely based semiring whose product with E is finitely based.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026twoelement,
  title = {{Two-element factors and finite bases for additively idempotent semirings}},
  author = {Qirui Ma and Mengya Yue},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21605},
  eprint = {2610.21605},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21605},
}
RIS
TY  - UNPB
TI  - Two-element factors and finite bases for additively idempotent semirings
AU  - Qirui Ma
AU  - Mengya Yue
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.21605
UR  - https://arxiv.org/abs/2610.21605
AB  - For every additively idempotent semiring S in the constant-free signature, S is finitely based if and only if S× E is finitely based when E=M_2 or T_2. For each E∈{L_2,R_2,D_2,N_2}, both implications fail even for finite S: we give a finite finitely based semiring whose product with E is nonfinitely based and a finite nonfinitely based semiring whose product with E is finitely based.
ER  -