# Ring Ann

• Nov 21st 2009, 12:45 PM
sfspitfire23
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 $\displaystyle X\subseteq Y$, show that $\displaystyle ann(Y)\subseteq ann(X)$

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

Thanks for any input guys.
• Nov 21st 2009, 06:47 PM
tonio
Quote:

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 $\displaystyle X\subseteq Y$, show that $\displaystyle ann(Y)\subseteq ann(X)$

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

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, $\displaystyle x\in Ann(Y)\,\Longrightarrow\,xy=0\,\,\forall\,y\in Y$...and as $\displaystyle X\subset Y$ then this is true in particular for all $\displaystyle x\in X$...etc.

Tonio