On the additive maps satisfying Skew-Engel conditions

Document Type: Research Paper

Authors

Department of Mathematics, Government College University, Lahore, Pakistan

Abstract

Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:I\rightarrow R$ be an additive
map. Then skew-Engel condition $\langle... \langle \langle$
$f(x),x^{n_1} \rangle,x^{n_2} \rangle ,...,x^{n_k} \rangle=0$ 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.

Keywords