关键词: 素环, 可导映射, 平方零元, 非平凡幂等元, 可加导子

Abstract: Let R be a unital prime ring containing a nontrivial idempotent, Q={T∈R: T2=0}, and R→R be a map (without additive assumption). Using method of algebraic decomposition, we prove that if δ(AB)=δ(A)B+Aδ(B) for any A,B∈R with ［A,B］B∈Q, then δ is an additive derivation, where ［A,B］=AB-BA is the Lie product.

Key words: prime ring, derivable map, square zero element, nontrivial idempotent, additive derivation