On rational functional identities
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Authors
Louisa Catalano
Tomas Merchan Rodriguez
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Journal Article, Academic Journal
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Abstract
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 $f(x)=-x^2g(x^{-1})$.