The Hua identity implies alternativity

Pasha Zusmanovich

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arXiv · 2609.30447

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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Pasha Zusmanovich. 2026-09-24. The Hua identity implies alternativity. https://arxiv.org/abs/2609.30447

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