Assume $S$ to be all continuous functions from $[0,1]$ to $\mathbb R$. I know by compactness of $[0,1]$ it follows that all maximal ideals of $S$ have the form $M_{x_0}=\{f\in S \mid f(x_0)=0\}$.Does there exist any non maximal prime ideal of $S$.I tried with some ideals of S but could not find any.please give me some idea how can I construct this?
2026-04-02 05:55:03.1775109303
Non Maximal Prime ideal!
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