In algebra, Hua's identity named after Hua Luogeng, states that for any elements a, b in a division ring, a − ( a − 1 + ( b − 1 − a ) − 1 ) − 1 = a b a {\displaystyle a-\left(a^{-1}+\left(b^{-1}-a\right)^{-1}\right)^{-1}=aba} whenever a b ≠ 0 , 1 {\displaystyle ab\neq 0,1} . Replacing b {\displaystyle b} with − b − 1 {\displaystyle -b^{-1}} gives another equivalent form of the identity: ( a + a b − 1 a ) − 1 + ( a + b ) − 1 = a − 1 .
In algebra, Hua's identity named after Hua Luogeng, states that for any elements a, b in a division ring, a − ( a − 1 + ( b − 1 − a ) − 1 ) − 1 = a b a {\displaystyle a-\left(a^{-1}+\left(b^{-1}-a\right)^{-1}\right)^{-1}=aba} whenever a b ≠ 0 , 1 {\displaystyle ab\neq 0,1} . Replacing b {\displaystyle b} with − b − 1 {\displaystyle -b^{-1}} gives another equivalent form of the identity: ( a + a b − 1 a ) − 1 + ( a + b ) − 1 = a − 1 .
Source: Wikipedia "Hua's identity" · CC BY-SA 4.0
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