In algebra, Hua's identity 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. 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.