Let $R$ be the ring of continuous functions on $[0,1]$ and let $I=\{f \in R\mid f(1/3) = f(1/2) = 0\}$. Then $I$ is an ideal but is not prime.
Please help me prove this, thank you.
Let $R$ be the ring of continuous functions on $[0,1]$ and let $I=\{f \in R\mid f(1/3) = f(1/2) = 0\}$. Then $I$ is an ideal but is not prime.
Please help me prove this, thank you.