Abstract:

Under some mild conditions on a unital ring R, we show that every additive map δ from R into itself satisfies δ(S。T)=δ(S)。T+S。δ(T) for any S,T∈R with ST=P if and only if δ is a Jordan derivation, where S。T=ST+TS is the Jordan product and P is a nontrivial idempotent of ring R.

Key words:  ring; Jordan derivation; Jordan derivable map