By results of Anderson and Slin’ko, derivations preserve the locally nilpotent and nil radicals of algebras over a field of characteristic 0. There is also a well known and elementary result that derivations preserve idempotent ideals. The radical results are extended to some (not all) rings, possible generalizations using generalizations of derivations are examined, the relevance of the result about idempotent ideals is pointed out and some comments about the Jacobson radical are included.