Nilpotency and nil subvarieties of binary Zinbiel algebras

@misc{smadyarov2026nilpotency,
  title = {{Nilpotency and nil subvarieties of binary Zinbiel algebras}},
  author = {Nurken Smadyarov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02852},
  eprint = {2610.02852},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02852},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Nilpotency and nil subvarieties of binary Zinbiel algebras
AU  - Nurken Smadyarov
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.02852
UR  - https://arxiv.org/abs/2610.02852
AB  - An algebra is called binary Zinbiel if every subalgebra generated by at most two elements is a Zinbiel algebra. Over a field of characteristic zero, we prove that every finite-dimensional binary Zinbiel algebra is nilpotent. We also show that a subvariety of binary Zinbiel algebras is nil if and only if it does not contain the variety of all Zinbiel algebras. We further prove an analogue of Itô's theorem for binary Zinbiel algebras.
ER  -