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 HairOnABiscuit December 9th, 2009 06:04 AM

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

 cknapp December 9th, 2009 06:25 AM

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.

 HairOnABiscuit December 12th, 2009 06:46 AM

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 $rx \in B$?

 mAraujo December 12th, 2009 01:11 PM

Re: Ideal

Quote:
 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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