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Let A be an algebra and M be a left A -module. We say that a linear mapping φ : A → M is a left derivable mapping at P if φ(ST ) = Sφ(T ) +Tφ(S) for any S,T ∈ A with ST = P . In this paper, we show that Jordan left derivations or left derivable mappings at zero or unit on some algebras are zero under certain conditions. Mathematics subject classification (2000): 47B47, 47L35.

Jordan left derivations and some left derivable maps