关于素环导子的几个定理  

Several theorem on derivations of prime rings

作　　者：于宪君[1] 

机构地区：[1]哈尔滨商业大学基础科学院,哈尔滨150076

出　　处：《哈尔滨商业大学学报（自然科学版）》2014年第3期319-320,共2页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：黑龙江省教育厅科学技术研究项目(11511105)

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.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 .

关 键 词：素环 导子 扭自由 交换性 

分 类 号：O153[理学—数学]