On a pair of (α, β)-derivations of semiprime rings

Summary.

Among other results we show that if α, β are centralizing epimorphisms and f, g are (α, β)-derivations of a 2-torsion free semiprime ring R such that f(x)x + xg(x) = 0 for all x ∈ R, then f(u)[x, y] = g(u)[x, y] = 0 for all x, y, u ∈ R; in particular, f and g map R into its center.