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 December 9th, 2009, 06:04 AM #1 Member   Joined: Oct 2009 Posts: 85 Thanks: 0 Ideal Let A and B be ideals of a ring R. Prove that (a) $A \cap B$ is an ideal of R (b) $A + B$ is an ideal of R
 December 9th, 2009, 06:25 AM #2 Senior Member   Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 Re: Ideal Check what happens if you multiply r (an arbitrary ring element) by an element of $A\cap B$ or an element of A+B.
 December 12th, 2009, 06:46 AM #3 Member   Joined: Oct 2009 Posts: 85 Thanks: 0 Re: Ideal Ok for part a) i need to show $rx \in A \cap B$ using $x \in A \cap B$ and $r \in R$. Proof: let $x \in A$ and $x \in B$, $r \in R$. How do i go form here to show that $rx \in A$ and $rx \in B$?
December 12th, 2009, 01:11 PM   #4
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Re: Ideal

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 Originally Posted by HairOnABiscuit How do i go form here to show that $rx \in A$ and $rx \in B$?
remember A and B are ideals of R.

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