On rational functional identities

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Louisa Catalano
Tomas Merchan
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In this paper, we progress in the general study of rational functional identities in the setting of division rings. The main theorem in the paper states that the only additive maps $f$ and $g$ satisfying that $f(x)=-x^ng(x^{-1}) $, for $n=3$ or $4$, are the zero maps. In addition, we provide an alternative proof to the result proved by Dar and Jing regarding the classification of additive maps $f$ and $g$ satisfying that $f(x)=-x^2g(x^{-1})$.
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