\\ $I'm having a little trouble determining a basis for the field extension $ \mathbb{Q}(e^{\frac{2 \pi i}{p}})/ \mathbb{Q} $ where p is any prime. I know $ [\mathbb{Q}(e^{\frac{2 \pi i}{p}}): \mathbb{Q}]=p-1. $ \\ Any pointers in the right direction would be greatly appreciated.$