Let $K$ be an algebraic number field. Prove that $O_K$ (collection of integral elements) contains infinitely many prime ideals.
Now this is Dedekind domain. Now what should be the next step?
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1What can you say about the simplest number field $\mathbf Q$? – Alex J Best Nov 04 '19 at 04:17
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$\Bbb Q(a)$ where $a$ is integral. Still not getting it!! – Ri-Li Nov 04 '19 at 05:56
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Please help me!!! – Ri-Li Nov 04 '19 at 05:57
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Alex was alluding to the ground field of rationals - why does the statement hold in this case? How could you go from there to any finite extension? – Hanno Nov 04 '19 at 06:26
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Can you please answer me in details – Ri-Li Nov 04 '19 at 07:44