[SOLVED] Ring Isomorphism - Math Help Forum

$Math Help Forum$

$Go Back$		Math Help Forum > University Math Help > Linear and Abstract Algebra
$Reload this Page$ [SOLVED] Ring Isomorphism

Download MHF Flyer

Mark Forums Read

$Reply$

#1

$Old$ November 17th, 2009, 09:35 AM

$sfspitfire23's Avatar$

sfspitfire23 $sfspitfire23 is online now$

Member

Join Date: Oct 2009

Posts: 100

Country:

Canada

Thanks: 47

Thanked 1 Time in 1 Post

$sfspitfire23 is on a distinguished road$

$Default$ [SOLVED] Ring Isomorphism

Q and R (reals and rationals) are not isomorphic because some elements in R are not division rings correct? (such as pi)?

$Reply With Quote$

Advertisement

#2

$Old$ November 17th, 2009, 11:22 AM

$Swlabr's Avatar$

Swlabr $Swlabr is offline$

Senior Member

Join Date: May 2009

Posts: 431

Country:

Scotland

Thanks: 44

Thanked 122 Times in 109 Posts

$Swlabr has a spectacular aura about$ $Swlabr has a spectacular aura about$

$Default$

Quote:

Originally Posted by sfspitfire23 $View Post$

Q and R (reals and rationals) are not isomorphic because some elements in R are not division rings correct? (such as pi)?

Unless I am much mistake, an element cannot be a division ring. It makes no sense!

Assume they are isomorphic, and let $\theta: \mathbb{R} \rightarrow \mathbb{Q}$ . Where is $2$ mapped to, and where is $\sqrt{2}$ mapped to?

(I am assuming you mean not isomorphic as rings, and not as groups?)

__________________

To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.

$Reply With Quote$

#3

$Old$ November 17th, 2009, 03:39 PM

$sfspitfire23's Avatar$

sfspitfire23 $sfspitfire23 is online now$

Member

Join Date: Oct 2009

Posts: 100

Country:

Canada

Thanks: 47

Thanked 1 Time in 1 Post

$sfspitfire23 is on a distinguished road$

$Default$

Ah, sorry, I mean the rings Q and R.

$Reply With Quote$

$Reply$

« solve for z & a | Top | Surjective function proof »

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are Off

Forum Jump

All times are GMT -7. The time now is 09:54 PM.

your link here Sponsors

rv solar, e-learning,

Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.