Rings with an additive rank function

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On Identities with Additive Mappings in Rings

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

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ژورنال

عنوان ژورنال: Journal of Algebra

سال: 1990

ISSN: 0021-8693

DOI: 10.1016/0021-8693(90)90280-2