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Math Help - Ideals of R

  1. #1
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    Ideals of R

    Would appreciate so much if anyone could show me how to this questions (exam tomorrow ah!)

    Consider the ring R=Z[X] and let

    I={f(X) in R : f(X)= 9g(X)+(X^2 -1)h(X) for some g(X),h(X) in R}

    be the ideal of R generated by the elements 9 and X^2 -1

    a. find all the ideals of R which contain I

    b. For every maximum ideal J of R containing I, use the fundamental isomorphism theorem for rings to prove the quotient ring R/J is isomorphic to Z3 (3 is a lower subscript)

    Thank you!
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  2. #2
    Super Member
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    Athens, OH, USA
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    Re: Ideals of R

    Hi,
    I delayed answering until after your exam so the attached answer did not give you an unfair advantage.

    Ideals of R-mhfring3.png
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