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Math Help - Ideal

  1. #1
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    Ideal

    Let R be a commutative ring with ideals I,J such that I J R. Show that J/I is an ideal of R/I.

    I am not sure how to begin. Thanks in advance for any help.
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  2. #2
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    Quote Originally Posted by page929 View Post
    Let R be a commutative ring with ideals I,J such that I J R. Show that J/I is an ideal of R/I.

    I am not sure how to begin. Thanks in advance for any help.

    Prove that J/I is an additive subgroup of R/I and that (r+I)(j+I)\in J/I\,\,\,\forall\,r+I\in R/I

    Tonio
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  3. #3
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    You do know what J/I means, right? I've seen some people get stuck with this simply from not knowing what is meant by "an ideal mod an ideal".
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  4. #4
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    I don't think that I do. Can you explain it to me?
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  5. #5
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    As a set, J/I=\{j+I\mid j\in J\}. They're the cosets in R/I whose representatives come from J. Notice that it makes sense to discuss this since I\subseteq J.
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