# Tagged Questions

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### Real analysis based on rings and ideals [duplicate]

Let $R$ be the ring of all the real valued continuous functions on the closed unit interval. Show that $M=\{ f\in R:f(1/3)=0 \}$ is a maximal ideal
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Let $R$ be a ring (not necessarily commutative) or an algebra over some field with a norm defined on it and let $I$ be an ideal in $R$. Let $a,b \in R$. Does it hold that $\inf_{i,j \in I}\|ab + ai ... 3answers 137 views ### Prime ideals in$C[0,1]$Are there any prime ideals in the ring$C[0,1]$of continuous functions$[0,1]\rightarrow \mathbb{R}$, which are not maximal? Perhaps, I duplicate smb's question, but this is an interesting problem! ... 1answer 183 views ### Ideal in compact Hausdorff space This is exercise 70, chapter 4. from Folland (page 142) Let$X$be a compact Hausdorff space. An ideal in$C(X, \mathbb{R})$is a subalgebra$J$of$C(X, \mathbb{R})$such that if$f\in J$and$g\in ...
Let $C(\mathbb R)$ denote the ring of all continuous real-valued functions on $\mathbb R$, with the operations of pointwise addition and pointwise multiplication. Which of the following form an ideal ...
Let $A = C^\omega(S^1)$ (resp. $C^\omega_{\mathbb C}(S^1)$) the ring of real-analytic real-valued (resp. complex valued) functions on the circle. These rings have maximal ideals \$\mathfrak m_p = ...