Abstract
Let D be a noncommutative division ring. In a recent paper, Lee and Lin proved that if charD≠2, the only solution of additive maps f,g on D satisfying the identity f(x)=xng(x−1) on D∖{0} with n≠2 a positive integer is the trivial case, that is, f=0 and g=0. Applying Hua's identity and the theory of functional and generalized polynomial identities, we give a complete solution of the same identity for any nonnegative integer n if charD=2.
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