My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum


Thanks Tree7Thanks
Reply
 
LinkBack Thread Tools Display Modes
April 20th, 2018, 12:14 PM   #1
Senior Member
 
Joined: Jan 2015
From: usa

Posts: 101
Thanks: 0

Isomorphism

Can you please help me with the question b) of the following problem? thanks in avance
Attached Images
File Type: jpg exercice3.jpg (15.1 KB, 45 views)
mona123 is offline  
 
April 20th, 2018, 02:29 PM   #2
Senior Member
 
Joined: Jan 2015
From: usa

Posts: 101
Thanks: 0

Please help me to prove that

$$h: (J:I)\rightarrow \text{Hom}_R(R/I, R/J)$$
$$x\mapsto h_x$$
where
$$h_x:R/I\rightarrow R/J$$
$$r+I\mapsto xr+J$$
is well defined
mona123 is offline  
April 20th, 2018, 02:57 PM   #3
Senior Member
 
Joined: Aug 2012

Posts: 1,889
Thanks: 525

Quote:
Originally Posted by mona123 View Post
Please help me to prove that

$$h: (J:I)\rightarrow \text{Hom}_R(R/I, R/J)$$
$$x\mapsto h_x$$
where
$$h_x:R/I\rightarrow R/J$$
$$r+I\mapsto xr+J$$
is well defined
What work have you done? Where are you stuck? It's inappropriate to ask questions at this level without showing that you've done any work of your own.

FWIW, relative to the ongoing moderation discussions, I'll take a thousand cranks and nuts rather than people repeatedly asking upper-division questions without showing any work.
Maschke is offline  
April 20th, 2018, 02:59 PM   #4
Senior Member
 
Joined: Jan 2015
From: usa

Posts: 101
Thanks: 0

we need to show that

$$r+I=r'+I \implies xr+J=xr'+J$$


for all $x\in (J:I)$
but i don't manage to do that
mona123 is offline  
April 20th, 2018, 03:26 PM   #5
Senior Member
 
Joined: Oct 2009

Posts: 403
Thanks: 139

Quote:
Originally Posted by Maschke View Post
FWIW, relative to the ongoing moderation discussions, I'll take a thousand cranks and nuts rather than people repeatedly asking upper-division questions without showing any work.
Seriously? You compare "integration" with THIS?
Micrm@ss is offline  
April 20th, 2018, 04:56 PM   #6
Senior Member
 
Joined: Aug 2012

Posts: 1,889
Thanks: 525

Quote:
Originally Posted by Micrm@ss View Post
Seriously? You compare "integration" with THIS?
I did not make a comparison. I said that I prefer one thing to another thing. A statement of preference can't be wrong, it's nothing more than my preference. I did not ask anyone else to share my personal preference.

I'm not a fan of integration, but I'm REALLY not a fan of posters who repeatedly ask upper-division or early grad-level question and NEVER show any work of their own.

That's my personal preference. It's not an endorsement of integration's posts. It's a statement of what frosts my butt. One thing frosts my butt more than another thing. Your butt frosting may vary. You should click through the OP's posts to get a sense of what I mean. I'm not basing my remarks on one post.

For the record I don't mean to bash one particular poster, this OP just happened to show up the same day that there's a discussion of moderation policies. And again, why is the Mariga thread still going on? That one frosts my butt too. Damn my butt is getting cold.

Last edited by Maschke; April 20th, 2018 at 05:01 PM.
Maschke is offline  
April 20th, 2018, 05:01 PM   #7
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 379
Thanks: 205

Math Focus: Dynamical systems, analytic function theory, numerics
Quote:
Originally Posted by Micrm@ss View Post
Seriously? You compare "integration" with THIS?
I'm not sure I would go so far as to prefer the crackpots over this, but I agree 99% with Maschke on this. Its absolutely absurd to be working at this level of math and still be unable to ask a more pointed questions than simply repeating the exercise. Mona's reply to his question is also completely unsatisfactory as it is nothing more than a restatement of the original question.
Thanks from Maschke
SDK is offline  
May 11th, 2018, 12:38 PM   #8
Senior Member
 
Joined: Aug 2017
From: United Kingdom

Posts: 188
Thanks: 57

Math Focus: Algebraic Number Theory, Arithmetic Geometry
Quote:
Originally Posted by mona123 View Post
we need to show that

$$r+I=r'+I \implies xr+J=xr'+J$$


for all $x\in (J:I)$
but i don't manage to do that
Try thinking about it for more than 3 seconds before asking on a forum. This is practically immediate from the definition $(J:I)$...
cjem is offline  
May 14th, 2018, 03:11 PM   #9
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,364
Thanks: 100

What's so advanced about the OP? It's no more difficult than Pinochle. It's just a matter of definitions.

Commutative ring is a straightforward set of elementary definitions you could teach in grammar school.

What is the definition of the triangle? Is that what makes something advanced, an undefined symbol?
zylo is offline  
May 14th, 2018, 08:57 PM   #10
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,364
Thanks: 100

Quote:
Originally Posted by cjem View Post
Try thinking about it for more than 3 seconds before asking on a forum. This is practically immediate from the definition $(J:I)$...
How does definition of (J:I) answer question b), which involves many more complicated definitions?

Definitions:

$\displaystyle \triangleleft$ Ideal: Ideal -- from Wolfram MathWorld

R/I is a quotient ring: Couldn't find a coherent definition.
From: Quotient Ring -- from Wolfram MathWorld
"A quotient ring (also called a residue-class ring) is a ring that is the quotient of a ring A and one of its ideals a, denoted A/a."
But qotient in this context is undefined.

Add to this the notation in b) of OP, which I couldn't google, and you are in the bowells of abstract pinochle.

Drilling down through all the definitions I find uninstructive, and impossible to remember and create a coherent picture.

But just out of curiousity, I would like to see a clean proof of OP b) with the steps referenced to approbriate definitions.


No matter what the topic, if the problem can be completely ensconced in a small set of intelligible definitions, it is interesting and educational, in spite of what Maschke says. I thought this might be the case here, but I see now that it would have been impossible for OP to even describe the problem in anything other than symbolism.
Thanks from topsquark
zylo is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
isomorphism



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Isomorphism mathbalarka Abstract Algebra 2 November 4th, 2012 10:53 PM
isomorphism tiger4 Abstract Algebra 2 July 2nd, 2012 02:17 AM
Isomorphism jpav Abstract Algebra 6 July 11th, 2011 06:00 AM
Isomorphism mia6 Linear Algebra 1 November 10th, 2010 08:31 AM
Isomorphism just17b Abstract Algebra 4 December 18th, 2007 07:57 AM





Copyright © 2018 My Math Forum. All rights reserved.