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I want to define \mathbb{Q}_p (\sqrt{5}) a nd \mathbb{Q}_p (\sqrt{5} \sqrt{3}) and find their valuation rings for p=7

I tried finite extension \mathbb({Q}_p I unable do it. it will also great if help me with how to define the valuation ring of that finite extension

I want to define \mathbb{Q}_p (\sqrt{5}) a nd \mathbb{Q}_p (\sqrt{5} \sqrt{3}) and find their valuation rings for p=7

I tried finite extension \mathbb({Q}_p I unable do it. it will also great if help me with how to define the valuation ring of that finite extension

I want How to define \mathbb{Q}_p (\sqrt{5}) a nd \mathbb{Q}_p $\mathbb{Q}_p(\sqrt{5})$ and $\mathbb{Q}_p (\sqrt{5} \sqrt{3}) \sqrt{3})$ and find their valuation rings for p=7$p=7$?

I tried finite extension \mathbb({Q}_p $\mathbb({Q}_p$ I unable do it. it It will also great if help me with how to define the valuation ring of that finite extension extension

How to define $\mathbb{Q}_p(\sqrt{5})$ and $\mathbb{Q}_p (\sqrt{5} \sqrt{3})$ and find their valuation rings for $p=7$?

I tried finite extension $\mathbb({Q}_p$ I unable do it. It will also great if help me with how to define the valuation ring of that finite extension

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How to define $\mathbb{Q}_p(\sqrt{5})$ and $\mathbb{Q}_p (\sqrt{5} \sqrt{3})$ and find their valuation rings for $p=7$?

I tried finite extension $\mathbb({Q}_p$ I unable do it. It will also great if help me with how to define the valuation ring of that finite extension

click to hide/show revision 6
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How to define $\mathbb{Q}_p(\sqrt{5})$ and $\mathbb{Q}_p (\sqrt{5} \sqrt{3})$ and find their valuation rings for $p=7$?

I tried finite extension $\mathbb({Q}_p$ I unable do it. It will also great if help me with how to define the valuation ring of that finite extension