# Homework Help: How to interpret quotient rings of gaussian integers

1. Feb 24, 2013

### nateHI

1. The problem statement, all variables and given/known data

This is just a small part of a larger question and is quite simple really. It's just that I want to confirm my understanding before moving on.

What are some of the elements of $Z/I$ where I is an ideal generated by a non-zero non-unit integer. For the sake of argument, lets take I=<3>.

2. Relevant equations

3. The attempt at a solution
Representatives from one coset would be the following...
(8+4i)/<3>=(5+i)/<3>=(2+i)$\in Z/<3>$

Representatives from another coset would be the following...
(7+5i)/<3>=(4+2i)/<3>=(1+2i)$\in Z/<3>$

2. Feb 24, 2013

### micromass

At first glance I think it would be $\mathbb{Z}_3$. Can you try to prove this?

3. Feb 24, 2013