Characterization of Δ-Double Derivations on Rings and Algebras

The main purpose of this article is to offer some characterizations of δ-double derivations on rings and algebras. to reach this goal, we prove the following theorem:let n>1 be an integer and let r be an n!-torsion free ring with the identity element 1. suppose that there exist two additive mappings d,δ:r→r such that d(xn)=σnj=1xn−jd(x)xj−1+σn−2k=0σn−2−ki=0xkδ(x)xiδ(x)xn−2−k−i is fulfilled for all x∈r. if δ(1)=0, then d is a jordan δ-double derivation. in particular, if r is a semiprime algebra and further, δ2(x2)=δ2(x)x+xδ2(x)+2(δ(x))2 holds for all x∈r, then d−12δ2 is an ordinary derivation on r.