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Math Help - Annihilator

  1. #1
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    Annihilator

    I am having problems showing X\subseteq ann(ann(X)). I don't understand how I would start this problem and don't understand what the annihilator of an annihilator would be.

    Thanks for the help!
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  2. #2
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    Quote Originally Posted by Kiwili49 View Post
    I am having problems showing X\subseteq ann(ann(X)). I don't understand how I would start this problem and don't understand what the annihilator of an annihilator would be.

    Thanks for the help!

    Let x\in X\Longrightarrow nx=0\,\,\,\forall\,n\in Ann(X)\Longrightarrow\,x annihilates every n\in Ann(X)\Longrightarrow\,x\in\,Ann(Ann(X))

    Tonio
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  3. #3
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    That is really helpful! I am still lost, though, on the last implication.
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  4. #4
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    Quote Originally Posted by Kiwili49 View Post
    That is really helpful! I am still lost, though, on the last implication.

    I can't make it clearer than that. I think you must check your definitions and make sure you understand them well: the proof is exactly in my post!

    Tonio
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