素环的T-对称双导

T-SYMMETRIC BI-DERIVATIONS OF PRIME RINGS

设R是一环 ,称D :R×R→为R的一个T_对称双导 ,如果它满足 (ⅰ )D(x,y) =D(y ,x) ;(ⅱ )D(x+y ,z) =D(x ,z) +D(y ,z) ;(ⅲ )D(xy ,z) =D(x ,z)T(y) +T(x)D(y ,z) .其中T为R的非恒等自同态 .该文研究素环T 对称双性质 ,得出两个主要结论 。

Let R be a ring with center Z(R). A mapping D:R×R→R is called a T-symmetric bi-derivation, if D(x,y)=D(y,x), D(x+y,z)=D(x,z)+D(y,z), and D(xy,z)=D(x,z)T(y)+T(x)D(y,z) for all x,y,z∈R, where T is a non-identity endomorphism of R. In this paper, the properties of T-symmetric bi-derivation of prime rings are studied and two main results are obtained.