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The Hua identity implies alternativity
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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