Zhang Jian-hua
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.
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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 concepts: Idempotence, Unital, Mathematics, Ring (chemistry), Combinatorics, Product (mathematics), Pure mathematics, Algebra over a field