Annihilators of derivations with Engel conditions on lie ideals

Generalized Skew Derivations With Annihilating Engel Conditions

“…Then a = 0 or δ = 0 except when R = M 2 (GF (2)). This result generalizes several known results, see for instance, [12], [13] and [16]. In this paper we will extend [7] further to the so-called right generalized skew derivations.…”

“…and hence a[c, x] k+1 = 0 for all x ∈ R. By a result of Shiue [16], we can conclude that a = 0 or c ∈ Z, which is a contradiction. So there exists v 0 ∈ V such that v 0 and cv 0 are C-independent.…”

Skew derivations with annihilating Engel conditions

“…Recently, Filippis [7] proved the following: Let R be a prime ring of characteristic different from 2, d a nonzero derivation and L a noncentral Lie ideal of R. For a ∈ R, if a [d(u), u] = 0 for all u ∈ L, then a = 0. That is, the left annihilator of the set [20] generalized this result by imposing the condition:…”

Annihilators of skew derivations with Engel conditions on prime rings

“…Then a = 0 or δ = 0 except when R = M 2 (GF (2)). Also in [24] Shiue obtained: Let R be a prime ring, L a noncentral Lie ideal of R and a…”