哈尔滨商业大学学报（自然科学版）
哈爾濱商業大學學報（自然科學版）
합이빈상업대학학보（자연과학판）
JOURNAL OF HARBIN UNIVERSITY OF COMMERCE(NATURAL SCIENCES EDITION)
2014年
3期
319-320
,共2页
素环%导子%扭自由%交换性
素環%導子%扭自由%交換性
소배%도자%뉴자유%교환성
prime ring%derivation%torsion free%commutativity
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。
討論瞭素環理想上導子的性質，推廣改進瞭文獻[4]，[5]中的結果。證明瞭下麵定理，設R是2-扭自由的素環，I是R的非零理想，Z是環R的中心。若存在非零導子d，滿足對任意的x∈I均有[ x，d（ x2）]∈Z或對任意的x∈I均有x2· d（ x）∈Z且Z∩I≠｛0｝x2，則環R為交換環。
토론료소배이상상도자적성질，추엄개진료문헌[4]，[5]중적결과。증명료하면정리，설R시2-뉴자유적소배，I시R적비령이상，Z시배R적중심。약존재비령도자d，만족대임의적x∈I균유[ x，d（ x2）]∈Z혹대임의적x∈I균유x2· d（ x）∈Z차Z∩I≠｛0｝x2，칙배R위교환배。
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 .
