x Turn on thread page Beta
 You are Here: Home >< Maths

# ring homomorphism qu (easy) watch

1. hello there,
just wondering how you show the following.

If phi is a ring homorphism mapping R to S (which are both rings), how do I show that phi(-a) = -phi(a) ??? (for a E R)

2. We need to show that phi(-a) + phi(a) = 0. To do this use the fact that since phi is a homomorphism, phi(a+b) = phi(a)+phi(b) for all a,b in R. In particular,

phi(-a)+phi(a) = phi(a-a) = phi(0) = 0

as required.

(Note: to show phi(0) = 0 use the fact that phi(0) = phi(0+0) = phi(0)+phi(0))
3. thank you very much

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 11, 2006
Today on TSR

### University rankings 2019

Cambridge at number one

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams