query: In the ring of continuous functions $\mathbb{R} \to \mathbb{R}$, the set of all $f$ with $f(0) = 0$ is a maximal ideal.
positive_passages.docid: 29126
positive_passages.text: Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
negative_passages.docid: 97605
negative_passages.text: Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
negative_passages.docid: 116943
negative_passages.text: Proof for maximal ideals in $\mathbb{Z}[x]$
negative_passages.docid: 57198
negative_passages.text: How to show that a valuation ring has a unique maximal ideal?
negative_passages.docid: 100560
negative_passages.text: $X$ compact Hausdorff space, characterize the maximal ideals of $C(X)$
negative_passages.docid: 69869
negative_passages.text: if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
negative_passages.docid: 6646
negative_passages.text: A (non-artificial) example of a ring without maximal ideals
negative_passages.docid: 137675
negative_passages.text: Every proper ideal is contained in a maximal ideal, in a commutative ring with identity.
negative_passages.docid: 144623
negative_passages.text: Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
negative_passages.docid: 92089
negative_passages.text: If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
negative_passages.docid: 67237
negative_passages.text: Pull back image of maximal ideal under surjective ring homomorphism is maximal
negative_passages.docid: 17139
negative_passages.text: Ring of holomorphic functions
negative_passages.docid: 34183
negative_passages.text: An equivalent condition with $\{0\}$ being the only nilpotent ideal
negative_passages.docid: 119056
negative_passages.text: If in a UFD every maximal ideal is principal then it is a PID
negative_passages.docid: 149412
negative_passages.text: Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
negative_passages.docid: 44083
negative_passages.text: prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
negative_passages.docid: 95469
negative_passages.text: Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$