On the additive maps satisfying Skew-Engel conditions

Let R be a prime ring, I be any nonzero ideal of R and f:I\rightarrow R be an additivemap. Then skew-Engel condition \langle... \langle \langlef(x),x^{n_1} \rangle,x^{n_2} \rangle ,...,x^{n_k} \rangle=0 implies that f (x)=0 \forall\,x\in I provided 2\neq char (R)>n_1+n_2+...+n_k, where n_1,n_2,...,n_k are natural numbers. This extends some existing results. In the end, we also generalise this result in the setting of MA-semirings.

On the additive maps satisfying Skew-Engel conditions Keywords:

Additive map , prime ring , semiprime ring , MA-semiring