# Homework Help: When do quadratic polynomials generate the same ideal?

1. Apr 24, 2017

### Mr Davis 97

1. The problem statement, all variables and given/known data
When do two quadratic polynomials in $\mathbb{Z}_3 [x]$ generate the same ideal?

2. Relevant equations

3. The attempt at a solution
I feel like they generate the same ideal only when they have the same coefficients, but am not sure how to show this.

2. Apr 26, 2017

### Staff: Mentor

It's not necessary for your question, as you only asked about principal ideals. Nevertheless, is $\mathbb{Z}_3[x]$ a principle ideal domain?
Now to approach your question. As always, write down what is given, namely two ideals $I=\langle p(x) \rangle$ and $J=\langle q(x)\rangle$ with polynomials $p(x),q(x)\in \mathbb{Z}_3[x]$ and $I=J$. The latter means $p(x) \in J$ and $q(x) \in I$. What can you conclude from this?