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Describe explicitly $\text{spec}(\mathbb{R}[x])$ and $\text{spec}(\mathbb{C}[x])$, (where for a given ring $R$, $\text{spec}(R)$ is defined to be the set of all prime ideals of $R$).

I don't have an attampt or something to start with.

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closed as off-topic by user26857, Riccardo.Alestra, Javi, clathratus, Strants Mar 20 at 21:07

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  • $\begingroup$ You can start with the definition of $\operatorname{Spec}$. $\endgroup$ – lisyarus Mar 19 at 17:21
  • $\begingroup$ For a given ring $R$, $\text{spec}(R)$ is defined to be the set of all prime ideals of $R$. @lisyarus $\endgroup$ – J. Doe Mar 19 at 17:22
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Let $F = \mathbb R$ or $\mathbb C$. Since $F$ is a field, $F[x]$ is a principal ideal domain. What can you say about the prime ideals in a principal ideal domain?

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  • $\begingroup$ $F[x]$ is a PID thus each prine ideal is generated by an irreducible polynom, thanks. $\endgroup$ – J. Doe Mar 19 at 17:36

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