Abstract
Let Mn(F) denote the set of square matrices of size n over a field F with characteristics different from two. We say that the map f:Mn(F)→Mn(F) is additive if f(A+B)=f(A)+f(B) for all A,B∈Mn(F). The main goal of this paper is to prove that for n>2 there are no additive surjective maps T:Mn(F)→Mn(F) such that per(T(A))=det(A) for all A∈Mn(F). Also we show that an arbitrary additive surjective map T:Mn(F)→Mn(F) which preserves permanent is linear and thus can be completely characterized.
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