Additivity ofn-Multiplicative Maps on Alternative Rings

Let ℜ and ℜ′ be alternative rings. We study the additivity of n-multiplicative isomorphisms from ℜ onto ℜ′ and of n-multiplicative derivations of ℜ. We prove that, if ℜ contains a family of nontrivial idempotents satisfying Martindale's conditions, then these two maps are additives.