Let D:R[x]->R[x] be the derivative map defined by D(a+a1*x+a2*x^2+....+an*x^n)=a1+2a*2x+...+…(n)*a*x ^(n-1) Is this a homomorphism of rings? Isomorphism? Explain I have no idea about this. Thanks
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Originally Posted by zhupolongjoe Let D:R[x]->R[x] be the derivative map defined by D(a+a1*x+a2*x^2+....+an*x^n)=a1+2a*2x+...+…(n)*a*x ^(n-1) Is this a homomorphism of rings? Isomorphism? Explain I have no idea about this. Thanks Does $\displaystyle D(p(x)\cdot q(x))=D(p(x))\cdot D(q(x))\,\,\,for\,\,\,p(x),q(x)\in R[x]$ ? And if you REALLY have "no idea" about this read your notes/book. Tonio
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