Let F be the ring of continuous functions from $R$ to $R$. Let $A =\{f \in F \; | \; f(0)=0\}$ Show that $A$ is maximal in R.
28244
Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
38963
Ideals in ring of continuous functions $\mathcal{C}[0,1]$ ... NBHM- Algebra
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
86472
$f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
55243
When is the ring of continuous functions Noetherian?
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
108060
Suppose $f:[0,\infty]\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
38228
Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$