【摘 要】
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Let R be a ting, a,b∈ R, (D, α) and (G,β) be two generalized derivations of R.It is proved that if aD(x) = G(x)b for all x∈ R, then one of the following pos
【机 构】
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School of Sciences
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Let R be a ting, a,b∈ R, (D, α) and (G,β) be two generalized derivations of R.It is proved that if aD(x) = G(x)b for all x∈ R, then one of the following possibilities holds:(i) Ifeithera or b is contained in C, then α=β=0 and there exist p,q∈Qr(RC) such that D(x)=px and G(x)=qx for all x∈R ;(ii) If both a and bare contained in C, then either a =b = 0 or D and G are C-linearly dependent; (iii) If neither a nor b is contained in C, then there exist p,q∈ Qr(RC) and w∈ Qr(R) such that α(x)=[q,x] and β(x)=[x,p] for all x∈ R, whence D( x ) = wx - xq and G( x ) = xp + avx with v∈ C and aw- pb = 0 .
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