My Math Forum  

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

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
October 19th, 2016, 01:53 PM   #1
Joined: Oct 2016
From: USA

Posts: 2
Thanks: 0

Isomorphism proof help

How do I show that the function Φ(x)= x is an isomorphism from R+ ,• to R+ ,• ?
AR1 is offline  
October 23rd, 2016, 03:10 AM   #2
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,195
Thanks: 872

It looks to me that showing that the definition of "isomorphism" applies would be the obvious thing to do!

A function is an "isomorphism" from one algebraic structure, X, to another, Y, if and only if
1) It is "one-to-one" and "onto".
"one to one": if f(x)= f(y) then x= y. "onto": for any y in Y, there exist x in X such that f(x)= y. For any y in R, take x= y.

2) f(x+ y)= f(x)+ f(y).

3) f(x•y)= f(x)•f(y)

Since f, here, is the identity function all of those are trivial!
Country Boy is offline  

  My Math Forum > College Math Forum > Abstract Algebra

isomorphism, proof

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Isomorphism Help!! xsirmath Linear Algebra 0 December 15th, 2014 06:25 AM
Isomorphism bewade123 Abstract Algebra 2 February 14th, 2012 04:12 PM
Isomorphism jpav Abstract Algebra 6 July 11th, 2011 06:00 AM
transpose isomorphism proof guroten Linear Algebra 0 October 29th, 2009 01:59 PM
Isomorphism just17b Abstract Algebra 4 December 18th, 2007 07:57 AM

Copyright © 2018 My Math Forum. All rights reserved.