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The Hua identity implies alternativity

  • Pasha Zusmanovich
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Abstract

The well-known Hua identity a − (a−1 + (b−1 − a)−1)−1 = aba holds in any associative division ring. We prove, in a sense, a converse: if a (nonassociative) ring with unit and multiplicative inverses satisfies the Hua identity, then it is alternative.

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Cite

BibTeXRIS
BibTeX
@misc{zusmanovich2026identity,
  title = {{The Hua identity implies alternativity}},
  author = {Pasha Zusmanovich},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30447},
  eprint = {2609.30447},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30447},
}
RIS
TY  - UNPB
TI  - The Hua identity implies alternativity
AU  - Pasha Zusmanovich
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30447
UR  - https://arxiv.org/abs/2609.30447
AB  - The well-known Hua identity a − (a^−1 + (b^−1 − a)^−1)^−1 = aba holds in any associative division ring. We prove, in a sense, a converse: if a (nonassociative) ring with unit and multiplicative inverses satisfies the Hua identity, then it is alternative.
ER  -