Abstract
Let A be a prime ring of characteristic not 2, with center Z(A) and with involution *. Let S be the set of symmetric elements of A. Suppose that f:SâA is an additive map such that [f(x),f(y)]=[x,y] for all x,yâS. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map ÎŒ:SâZ(A) such that f(x)=x+ÎŒ(x) for all xâS or f(x)=-x+ÎŒ(x) for all xâS.
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