If $f(x) \in K[x]$ and $g(x) \notin K[x]$, can $f(x)g(x) \in K[x]$?
14270
Polynomial divisibility is unchanged by coeff. field extension
101773
Let $g : A \to B$ and $f : B \to C$ be functions. Let $f \circ g$ be onto. Are both $f$ and $g$ necessarily onto?
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
113385
Example of $f,g: [0,1]\to[0,1]$ and Riemann-integrable, but $g\circ f$ is not?
157840
Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
26424
If $f(x)<g(x)$ prove that $\lim f(x)<\lim g(x)$
83036
f(g(x)) has a degree divisible by n
156679
$K[X,Y]/(XY-1)$ not isomorphic to $K[T]$
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
147200
Given fields $K\subseteq L$, why does $f,g$ relatively prime in $K[x]$ imply relatively prime in $L[x]$?
89514
Show that if $g \circ f$ is injective, then so is $f$.
33576
Non-principal ideal in $K[x,y]$?
101042
Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
135046
Can this quick way of showing that $K[X,Y]/(Y-X^2)\cong K[X]$ be turned into a valid argument?
145507
Is $K[a,b]=K(a,b)$ for algebraic $a, b$?
63590
Let $g$ be a function from $(0, 1)$ to $\mathbb{R}$ and $\int_0^1 g^2(x)dx$ finite. Does this imply that $\int_0^1 g(x)dx$ is finite?