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Math Help - One more very confusing abstract algebra problem

  1. #1
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    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

    I have no idea about this. Thanks
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    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 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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