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Let $R=\mathcal{C}([0,1],\mathbb{R})$ be the ring (standard one) of continuous functions. For each $\gamma\in[0,1]$, let $I_\gamma=\{f\in R; f(\gamma)=0\}$. It is easy to prove that $I_\gamma$ is an ideal, in fact, a maximal one.

My question is: how to find other ideals (not necessarily maximal), that is, different of the type of $I_\gamma$?

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    Let $A\subseteq[0,1]$ be arbitrary, and let $I_A=\{f\in R:f(a)=0\text{ for all }a\in A\}$.2012-08-26
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    @BrianM.Scott, thanks fot the suggestion, but your ideal is made with the same idea, that is, functions that vanishes. I am looking for some different types of ideals.2012-08-26
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    @GerryMyerson, sorry, but I have to read many answers to my questions, and they are not so trivial. So I need time to accept them.2012-08-26
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    The answers at http://mathoverflow.net/questions/35793/prime-ideals-in-c0-1 might prove helpful. Good luck!2012-08-26
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    @FortuonPaendrag, thanks so much. Good link. For sure I'll learn a lot with it.2012-08-26
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    Well, ideals can be defined as kernels of ring homomorphisms. And this being a function ring, these are the obvious ring homomorphisms to the product rings.2012-08-26

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