In this paper, centralizing (semi-centralizing) and commuting (semi-commuting) derivations of semirings are characterized. The action of these derivations on Lie ideals is also discussed and as a consequence, some significant results are proved. In addition, Posner’s commutativity theorem is generalized for Lie ideals of semirings and this result is also extended to the case of centralizing (semi-centralizing) derivations of prime semirings. Further, we observe that if there exists a skew-commuting (skew-centralizing) derivation D of S, then D = 0. It is also proved that for any two derivations d1 and d2 of a prime semiring S with char S ≠ 2 and xd1xd2 = 0, for all x ∈ S implies either d1 = 0 or d2 = 0.
Albas, E. and Argac, N.Generalized derivations of prime rings. Algebra Colloquium11, 3 (2004), 399–410.
Albas, E. and Argac, N.Generalized derivations of prime rings. Algebra Colloquium 11, 3 (2004), 399–410.)| false