Hua's identity

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{{#invoke:Hatnote|hatnote}} In algebra, Hua's identity[1] states that for any elements a, b in a division ring,

whenever . Replacing with gives another equivalent form of the identity:

An important application of the identity is a proof of Hua's theorem.[2][3] The theorem says that if is a function between division rings and if satisfies:

then is either a homomorphism or an antihomomorphism. The theorem is important because of the connection to the fundamental theorem of projective geometry.

Proof

References

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