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Hua's identity

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In algebra, Hua's identity[1] states that for any elements a, b in a division ring,

whenever .

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

,

then is either a homomorphism or antihomomorphism.

Proof

.

References

  1. ^ Cohn 2003, §9.1
  2. ^ Cohn 2003, Theorem 9.1.3
  • Cohn, Paul M. (2003). Further algebra and applications. Springer. ISBN 1-85233-667-6.