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Is Q_r algebraically isomorphic to Q_s whilewhere r and s denote different primes?

It is obvious that Q_r$\mathbb{Q}_r$ is topologically isomorphic to Q_s while r$\mathbb{Q}_s$ where $r$ and s$s$ denote different primes.But But I really don't know whether it is true in the aspect of algebra.As As I failed to prove it,I I think that it is false,but but I can't give a counterexample. Last I'm quite sorry that I'm new to MathJax and I don't know how to use it properly.Thanks Thanks for reading and I would appreciate it if you could solve my problem.

Is Q_r algebraically isomorphic to Q_s while r and s denote different primes?

It is obvious that Q_r is topologically isomorphic to Q_s while r and s denote different primes.But I really don't know whether it is true in the aspect of algebra.As I failed to prove it,I think that it is false,but I can't give a counterexample. Last I'm quite sorry that I'm new to MathJax and I don't know how to use it properly.Thanks for reading and I would appreciate it if you could solve my problem.

Is Q_r algebraically isomorphic to Q_s where r and s denote different primes?

It is obvious that $\mathbb{Q}_r$ is topologically isomorphic to $\mathbb{Q}_s$ where $r$ and $s$ denote different primes. But I really don't know whether it is true in the aspect of algebra. As I failed to prove it, I think that it is false, but I can't give a counterexample. Last I'm quite sorry that I'm new to MathJax and I don't know how to use it properly. Thanks for reading and I would appreciate it if you could solve my problem.

Post Closed as "too localized" by user9198, Felipe Voloch, Chandan Singh Dalawat, GH from MO, Igor Rivin
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Is Q_r algebraically isomorphic to Q_s while r and s denote different primes?

It is obvious that Q_r is topologically isomorphic to Q_s while r and s denote different primes.But I really don't know whether it is true in the aspect of algebra.As I failed to prove it,I think that it is false,but I can't give a counterexample. Last I'm quite sorry that I'm new to MathJax and I don't know how to use it properly.Thanks for reading and I would appreciate it if you could solve my problem.