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.