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PreprintCC BY 4.0arXiv

The finite basis problem for all subvarieties of the variety V(S07)

  • Mengya Yue
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Abstract

We solve the finite basis problem for all subvarieties of V(S07). By considering their intersections with V(S7), we reduce the problem to six intervals. We show that V(S70) has exactly fifteen finitely based subvarieties and that every other subvariety is nonfinitely based. Moreover, V(Sc(abc)) and V(SR6) are the only limit subvarieties of V(S70).

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Cite

BibTeXRIS
BibTeX
@misc{yue2026finite,
  title = {{The finite basis problem for all subvarieties of the variety $\mathsfV(S^0_7)$}},
  author = {Mengya Yue},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25823},
  eprint = {2609.25823},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25823},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The finite basis problem for all subvarieties of the variety V(S^0_7)
AU  - Mengya Yue
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25823
UR  - https://arxiv.org/abs/2609.25823
AB  - We solve the finite basis problem for all subvarieties of V(S^0_7). By considering their intersections with V(S_7), we reduce the problem to six intervals. We show that V(S_7^0) has exactly fifteen finitely based subvarieties and that every other subvariety is nonfinitely based. Moreover, V(S_c(abc)) and V(SR_6) are the only limit subvarieties of V(S_7^0).
ER  -