| Abstrakt: |
Let A be a unital A-algebra containing a non-trivial projection. In this paper, we prove that if a map Ω: A → A such that Ω([K, F]A ⊙ D) = [Ω(K), F]A ⊙ D + [K, Ω(F)]A ⊙ D + [K, F]A ⊙ Ω(D), where [K, F]A = KF - FKA and K ⊙ F = KAF + FKA for all K, F, D ∈ A, then Ω is an additive A-derivation. Furthermore, we extend its results on factor von Neumann algebras, standard operator algebras and prime A-algebras. Additionally, we provide an example illustrating the existence of such maps. [ABSTRACT FROM AUTHOR] |
