摘要
Let R be a semiprime ring with the center Z(R), d and g be derivations of R, L be a nonzero left ideal of R and rR(L) = 0. Suppose that d(x)x - xg(x) ∈ Z(R) for all x ∈ L, then d(R) Z(R) and the ideal of R generated by d(R) is in the center of R.
本文讨论了微商作用在半素环的某些左理想上的问题.给出了如下结果:设R是带有中心Z（R）的半素环.d和g是R的微商,L为R的非零左理想且rR（L）=0.假设d（x）-xg（x）∈Z（R）对任意的x∈L成立.那么d（R） Z(R）且由d（R）生成的R的理想在R的中心里.
基金
Supported by the National Natural Science Foundation of China(19671035)
