%0 Journal Article %T On some additive mappings on division rings %J Journal of Algebra and Related Topics %I University of Guilan %Z 2345-3931 %A Ali, S. %A Abdelwanis, A. %D 2021 %\ 12/01/2021 %V 9 %N 2 %P 101-110 %! On some additive mappings on division rings %K Division ring %K Derivation %K $(alpha %K beta)$-derivation %K functional identity %R 10.22124/jart.2021.19142.1263 %X  Let $D$ be a division ring such that char$(D) \neq 2$  and $\alpha,\beta:D\rightarrow D$ be automorphisms of $D$. The main purpose of this paper is to characterizes additive maps                              $f$ and $g$ satisfying the identity $f(x)\alpha(x^{-1}) + \beta(x)g(x^{-1}) = 0$ for all $0 \neq x\in D.$ As an application, we describe the structure of an additive map $f$ satisfying the identity                            $f(x)\alpha(y)+\beta(x)f(y) =l$ for all $x,y\in D$ such that $xy=a,$ where $l,a\in D$ and $a$ is nonzero. With this, many known results can be either generalized or deduced. In particular, we generalized the results proved in\cite{C1} and \cite{C2}, respectively.                                                                                                                                                                                            %U https://jart.guilan.ac.ir/article_5303_664350d6c417e151b54114b0e421bdfc.pdf