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_۱} \rangle,x^{n_۲} \rangle ,...,x^{n_k} \rangle=۰ implies that f (x)=۰ \forall\,x\in I provided ۲\neq char (R)>n_۱+n_۲+...+n_k, where n_۱,n_۲,...,n_k are natural numbers. This extends some existing results. In the end, we also generalise this result in the setting of MA-semirings.

Keywords:

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