Hua's theorem for simple Artin algebras
Hua's theorem states that a bijection \(f\) of a skew field \(K\) satisfying \((a+b)f=af+bf\), \(If=1\), \((a^{-1})f\cdot af=1\) (\(a\neq 0\)) is an auto- or an antiautomorphism [\textit{L.-K. Hua}, Proc. Natl. Acad. Sci. USA 35, 386-389 (1949; Zbl 0033.10402)]. The authors establish the same result for the \(n\times n\) matrix ring over \(K\), for any \(n>1\), provided that \(K\) has more than 2 elements.
scientific article; zbMATH DE number 1400195