| Abstrakt: |
Let R be a prime ring, let 0 ≠ b ∈ R , and let α and β be two automorphisms of R. Suppose that F : R → R , F 1 : R → R are two b-generalized (α , β) -derivations of R associated with the same (α , β) -derivation d : R → R , and let G : R → R be a b-generalized (α , β) -derivation of R associated with (α , β) -derivation g : R → R . The main objective of this paper is to investigate the following algebraic identities: (1) F (x y) + α (x y) + α (y x) = 0 , (2) F (x y) + G (x) α (y) + α (y x) = 0 , (3) F (x y) + G (y x) + α (x y) + α (y x) = 0 , (4) F (x) F (y) + G (x) α (y) + α (y x) = 0 , (5) F (x y) + d (x) F 1 (y) + α (x y) = 0 , (6) F (x y) + d (x) F 1 (y) = 0 , (7) F (x y) + d (x) F 1 (y) + α (y x) = 0 , (8) F (x y) + d (x) F 1 (y) + α (x y) + α (y x) = 0 , (9) F (x y) + d (x) F 1 (y) + α (y x) - α (x y) = 0 , (10) [ F (x) , x ] α , β = 0 , (11) (F (x) ∘ x) α , β = 0 , (12) F ([ x , y ]) = [ x , y ] α , β , (13) F (x ∘ y) = (x ∘ y) α , β for all x , y in some suitable subset of R. [ABSTRACT FROM AUTHOR] |
