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Math Help - Rings and subrings

  1. #1
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    Rings and subrings

    Really struggling with this question.

    Let R=C[X] (complex)

    S={f(X) = (sum from i=0 to n) aiXi in C[X] : a2= 0} and
    T={f(X) = (sum from i=0 to n) aiXi in C[X] : a1= 0}

    S and T are the sets of polynomials with coefficients in C and with zero quadratic, respectively linear, term.

    Prove that S is not a subring of R
    Prove that T is a subring of R, but not an ideal or R.

    Any help much appreciated!!
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  2. #2
    Junior Member Nehushtan's Avatar
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    Re: Rings and subrings

    S is not closed under multiplication: X\in S but X^2\notin S.

    Showing that T is a subring is straightforward. It is not an ideal because 1\in T and X\in R but 1\cdot X\notin T.
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