# Thread: One more very confusing abstract algebra problem

1. ## One more very confusing abstract algebra problem

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

2. 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

Does $D(p(x)\cdot q(x))=D(p(x))\cdot D(q(x))\,\,\,for\,\,\,p(x),q(x)\in R[x]$ ?