# Math Help - Ring Ann

1. ## 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.

2. Originally Posted by sfspitfire23
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