# Math Help - Polynomial Rings over fields with characteristic p

1. ## Polynomial Rings over fields with characteristic p

Let $char(\mathbb{F}) = p$, where $\mathbb{F}$ is a field. For what fields is $\frac{\mathbb{F}}{}$ an integral domain?

I tried using the Frobenius homomorphism, but I kept going in circles. Any ideas on how to proceed? (and please no direct Galois theory, if possible, as I don't know any)

2. ## Re: Polynomial Rings over fields with characteristic p

F should be a field over which the polynomial is irreducible.