A Class Of Jordan Ring Can Guide Map

In this paper, under some mild conditions on a unital ring A, we mainly and detailedly discuss Jordan derivable mappings at idempotent of ring A.In Chapter1, we give some notions, definitions(for example, nest algebra, derivation. Jordan derivation) and some well-known theorems.In Chapter2, we discuss Jordan derivable mapping at trivial idempotent of certain rings. We prove that every Jordan derivable mapping at trivial idempotent of certain rings is a Jordan derivation.In Chapter3, we discuss Jordan derivable mapping at nontrivial idempotent of certain rings. We prove that every Jordan derivable mapping at nontrivial idempo-tent of certain rings is a Jordan derivation.