1. Jan 25, 2009

### caji

Hey,

If $$p \neq q$$ are two primes, then the p-adic fields $$\mathbb{Q}_p$$ and $$\mathbb{Q}_q$$ are non isomorphic, right?

Actually I've read this in my book and I'm not sure, if that's obvious (which means its just me who doesn't recognize it) or a statement which has to be proven.

The p-adic fields as I know them are defined as:
Let $$\mathcal{C}_p$$ be the set of all rational Cauchy-Sequences, and $$\mathcal{N}_p$$ be the ideal of $$\mathcal{C}_p$$ of all sequences converging to zero. Then $$\mathbb{Q}_p := \mathcal{C}_p / \mathcal{N}_p$$

caji