# Polynomial Rings over fields with characteristic p

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• May 22nd 2012, 01:40 PM
wsldam
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)
• May 25th 2012, 11:01 AM
sorv1986
Re: Polynomial Rings over fields with characteristic p
F should be a field over which the polynomial is irreducible.