【摘要】 讨论了素环理想上导子的性质,推广改进了文献[4],[5]中的结果.证明了下面定理,设R是2-扭自由的素环,I是R的非零理想,Z是环R的中心.若存在非零导子d,满足对任意的x∈I均有[x,d(x2)]∈Z或对任意的x∈I均有x2·d(x)∈Z且Z∩I≠{0}x2,则环R为交换环.更多还原

【Abstract】 Properties of ideals in prime rings with derivations were discussed. The results of the references of [4]and [5]were extended and improved. Following theorems were given.Let R be a prime rings with 2-torsion free,I was a nonzero ideal of R,and Z was the center of R. If there existed a nonzero derivation d such that[x,d( x) ]∈Z for all x∈I or x2·d( x) ∈Z,for all x∈I and Z∩I≠{ 0},then R was a commutative ring.更多还原