半素拟环Lie理想上的导子的研究

Properties of Derivations on Lie Ideals of Semi-Prime Quasi-Rings

环论是代数数论和几何的基础,现已被应用到很多领域.由于半素环比素环更具一般性,所以将素环上导子的性质推广到半素环上也具有重要的意义.文章证明了设R是中心为Z(R)的2-扭自由半素拟环,U Z(R)是R上的非零Lie理想.若d是R上的导子,且d(U)=0,则d=0.

Ring theory is the basis of algebraic number theory and geometry.It has now been applied to many fields.Since the semi-prime ring is more general than the prime ring.General,so it is also important to generalize the properties of the derivatives on the prime ring to the semi-prime ring.In the present paper it is shown that:if Ris 2-torsion free semi-prime quasi-ring,let Uthat does not belong to the center of the semi-prime quasi-ring be a nonzero Lie ideal of R,da derivation of R,ifd (U)=0,then d=0.