My Math Forum  

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

Abstract Algebra Abstract Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 4th, 2009, 09:04 PM   #1
Newbie
 
Joined: May 2009

Posts: 2
Thanks: 0

True/False about Homomorphisms and Zero Divisors

Which are true and false and why:

1) Let f : R --> S be a ring homomorphism, then an element r in R is a zero divisor if and only if f(r) is a zero divisor in S

2) Let f : R --> S be a ring homomorphism that is also surjective. If an element s in S is a zero divisor, then there exists an element r in R such that f(r)=s and r is a zero divisor in R.

3) Let f : R --> S be a ring homomorphism that is also surjective. Then f is a ring isomorphism if and only if the kernel of f contains only the zero element.
jkong05 is offline  
 
May 5th, 2009, 03:41 AM   #2
Senior Member
 
Joined: Oct 2007
From: Chicago

Posts: 1,701
Thanks: 3

Re: True/False about Homomorphisms and Zero Divisors

What have you tried so far?

3 is straightforward... Apply what you know about group homomorphisms.

1 and 2 are really similar.... Think about a really big ring being mapped to a really small ring. Actually... take f : Z --> Z_(n*m) and look at f(n) and f(m).

If that isn't enough, show us where you're stuck.
Cheers!
cknapp is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
divisors, homomorphisms, true or false



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
true or false bOw Algebra 2 May 27th, 2012 01:39 PM
true and false .? sam_17 Abstract Algebra 12 March 29th, 2012 03:27 PM
true or false??? shimaa Calculus 1 February 17th, 2012 12:45 PM
True or False and WHY? bradycat Algebra 2 January 31st, 2009 08:28 AM
true and false .? sam_17 Algebra 10 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.