ON THE ADDITIVE MAPS SATISFYING SKEW-ENGEL CONDITIONS

Let R be a prime ring, I be any nonzero ideal of R and f : I → R be an additive map. Then skew-Engel condition h...hh f(x), x^n1 i, x^n2 i, ..., x^nk i = 0 implies that f(x) = 0 ∀ x ∈ I provided 2 ≠ char (R) n1 + n2 + ... + nk, where n1, n2, ..., nk are natural numbers. This extends some existing results. In the end, we also generalise this result in the setting of MA-semirings.