Additive mapping acting as generalized (mu; nu)-derivation on semi-prime rings

The objective of this paper is to study the following: Let A be a (m+n 1)-torsion free semi-prime ring. Suppose that G; g : A A are two additive mappings satisfying the algebraic identity G(rm+n) = G(rm)(rn) + (rm)g(rn)for all r 2 A: Then G will be a generalized (; )-derivation with associated (; )-derivation g on A. On the other hand, it is proved that G1 is a generalized left (; )-derivation associated with left (; )-derivation g1 on A if they satisfy the algebraic identity G1(rm+n) = (rn)G1(rm) + (rm)g1(rn) for all r 2 A. We will also examine criticism and provide example.