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Math Help - Determine the number of Elements

  1. #1
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    Determine the number of Elements

    HELP!!!!
    Let A denote the ideal of Z3[x] generated by the polynomial x^2+x+1, that is,

    A={f(x)(x^2+x+1)|f(x) is an element of Z3[x]},

    Determine the number of elements in the factor ring Z3[x]/A.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Determine the number of Elements

    Quote Originally Posted by fourth View Post
    HELP!!!!Let A denote the ideal of Z3[x] generated by the polynomial x^2+x+1, that is, A={f(x)(x^2+x+1)|f(x) is an element of Z3[x]}. Determine the number of elements in the factor ring Z3[x]/A.
    Hint: p(x)+A=q(x)+A\Leftrightarrow p(x)-q(x)\in A . Now use the euclidean division to prove that every element \mathbb{Z}_3/A can be uniquely expressed by p_1(x)+A with \textrm{deg}(p_1(x))<2 .


    Edited: Of course I meant \mathbb{Z}_3[x]/A instead of \mathbb{Z}_3/A .
    Last edited by FernandoRevilla; August 16th 2011 at 10:52 AM.
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