# Irreducible polynomial, cyclic group

1. Dec 9, 2008

### mathsss2

Describe the field $$F=\frac{\mathbb{F}_3[x]}{(p(x))}$$ [$$p(x)$$ is an irreducible polynomial in $$\mathbb{F}_3[x]$$]. Find an element of $$F$$ that generates the cyclic group $$F^*$$ and show that your element works.

[$$p(x)=x^2+1$$ is irreducible in $$\mathbb{F}_3[x]$$ if that helps]

2. Dec 9, 2008

### Hurkyl

Staff Emeritus
I've already given you a warning about posting your homework questions without showing your attempts to work on the problem. Continuing to do so will not be tolerated.

3. Dec 9, 2008