If $f \in R[x]$ factors in $S[x]$ as $f(x) =g(x)h(x)$ with $g(x)$ a monic polynomial in $R[x]$, then $h$ is also in $R[x]$.
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
89514
Show that if $g \circ f$ is injective, then so is $f$.
41810
Should all polynomial functions from F to F (F is a field) have coefficients in F?
152721
Help showing $H_n=\sum_{h \in H}h \in F[H]$ is a simple submodule
37593
Can all real polynomials be factored into quadratic and linear factors?
6722
to show $f$ is a polynomial in $z$
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
121404
How to factor polynomials in $\mathbb{Z}_n$?
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
95976
Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG?
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
10254
Is the Polynomial Factor Theorem true over all commutative rings?
18126
If $f \colon [a,b] \rightarrow \mathbb{R}$, then show that there exists $c \in [a,b]$ such that $\int_a^c f = \int_c^b f$
68071
If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.
146506
If a complex function $f$ is Entire, and there exist $k,R > 0$, $n \in N$ such that $|f(z)| > k|z|^n$ for all $|z| > R$, then f is a polynomial.
114762
Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible.
122958
$R/I$ is commutative iff $rs-sr \in I$