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Thread: Union ideals

  1. #1
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    Union ideals

    Hl!. I have problems with exercice


    Let I and J be ideals in a commutative ring R . Prove that their union I \cup{J} is a ideal if and only if I\subseteq{J} or J\subseteq{I}

    Hint please


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  2. #2
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    Re: Union ideals

    If y is in J but not in I and x is in I but not in J, consider x+y
    Thanks from cristianoceli
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  3. #3
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    Re: Union ideals

    Suppose i is in I but not in J. Suppose j is in J but not in I.

    If I\cup J is an ideal, then i+j\in I\cup J, but i+j\in I implies ________ and i+j\in J implies _________. Any contradictions?

    I will admit my knowledge of commutative algebra is less than ideal these days.
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  4. #4
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    Re: Union ideals

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