On (m, n)-derivations of Some Algebras

Let $\mathcal{A}$ be a unital algebra, $δ$ be a linear mapping from $\mathcal{A}$ into itself and $m$, $n$ be fixed integers. We call $δ$ an (\textit{m, n})-derivable mapping at $Z$, if $mδ(AB)+nδ(BA)=mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A)$ for all $A, B\in \mathcal{A}$ with $AB=Z$. In this paper, (\textit{m, n})-derivable mappings at 0 (resp. $I_\mathcal{A}\oplus0$, $I$) on generalized matrix algebras are characterized. We also study (\textit{m, n})-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.

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