Notation of ideals in ring theory

1. Mar 4, 2007

erraticimpulse

So right now i'm trying to solve this problem in ring theory for homework. The question pertains to proving that in a PID, D, if a,b are elements of D then the gcd of a and b can be written as a linear combination. In any event I know where I have to go but I'm stuck on this one bit of notation.

<a,b> = <d>.

I've never seen notation for an ideal like that with 2 elements separated by a comma. I'd appreciate any insight into this.

Oh and here's the site from wolfram where I originally discovered it:
http://mathworld.wolfram.com/PrincipalIdealDomain.html

2. Mar 4, 2007

ZioX

<a,b> is any linear combination of a and b.

That is, <a,b>={as+bt|s,t are in R}

3. Mar 4, 2007

erraticimpulse

Thanks man. You rock my socks!

4. Mar 4, 2007

erraticimpulse

Okay well, it turned out that the idea from wolfram was more confusing than helpful. There's a scarce amount of information in my text and notes on PID's. The only conjectures that I feel safe in making: if given gcd(a,b)=d then gcd(a,d)=d and gcd(b,d)=d. Not sure how helpful those are though. I think what I'm most confused about is Wolfram's assertion that <a,b> is an ideal for any a,b. I can't verify this anywhere.

5. Mar 4, 2007

erraticimpulse

Nevermind, I figured it out. Thanks for the insight Ziox!