素环上的左Jordan导子

On Left Jordan Derivations of Simple Rings

研究了素环上的左Jordan导子,利用素环的性质和已有结论证明了R为2-非挠的素环,若D为R→R的左Jordan导子,则D为R→Z(R)上的一个导子,从而在素环上得到了一个良好的保持性结论。

Left Jordan derivation on simple rings are studied. Using the properties of prime ring and the existed resuits, it is proved that if R is a 2-torsion free prime ring and D ： R→R is a left Jordan derivation then D is a derivation which maps R to Z （R）. Thus a good mapping keeping conclusion on prime rings are gived.