Hua's identity

In algebra, Hua's identity named after Hua Luogeng, states that for any elements a, b in a division ring,

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

Hua's theorem

The identity is used in a proof of Hua's theorem, which states that if is a function between division rings satisfying

then is a homomorphism or an antihomomorphism. This theorem is connected to the fundamental theorem of projective geometry.

Proof of the identity

One has

The proof is valid in any ring as long as are units.

References