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Math Help - Ring Ann

  1. #1
    Senior Member sfspitfire23's Avatar
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    Ring Ann

    Alright, I know how to show an annihilator is an ideal. I have a been working on these next problems for a bit, trying to see if I'm close

    1. If X\subseteq Y, show that ann(Y)\subseteq ann(X)

    2. Show that ann(X\cup Y)=ann(X)\cap ann(Y)


    Thanks for any input guys.
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  2. #2
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    Quote Originally Posted by sfspitfire23 View Post
    Alright, I know how to show an annihilator is an ideal. I have a been working on these next problems for a bit, trying to see if I'm close

    1. If X\subseteq Y, show that ann(Y)\subseteq ann(X)

    2. Show that ann(X\cup Y)=ann(X)\cap ann(Y)


    Thanks for any input guys.

    Well, if you've really been working on these for a bit then I can't understand where the problem is...for example, x\in Ann(Y)\,\Longrightarrow\,xy=0\,\,\forall\,y\in Y...and as X\subset Y then this is true in particular for all x\in X...etc.

    Tonio
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