# 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

Not to mention this should be in the Abstract Algebra forum.

Write the elements of F explicitly (in terms of, say, t, where t2 + 1 = 0). Find one that has order 8.