0
votes
2answers
42 views

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
0
votes
2answers
131 views

Are the two infima equal?

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 ...
6
votes
4answers
166 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! ...
9
votes
1answer
188 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 ...
0
votes
1answer
298 views

multiple choice question for compact support functions.

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 ...
2
votes
1answer
207 views

Ring of analytic functions on the circle

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 = ...