If $k[X]/f = k[X]/g$, does $f = g$?
47114
What is necessary and/or sufficient for polynomials to provide isomorphic quotient rings?
11698
$M /K \land L /K$ algebraic $\implies ML/K$ algebraic?
65744
How can I Prove that H=G or K=G
140095
Let $k^p = k$, $K = k(x)$ and $F = k(u)$ for some $u \in K$. Show that $K/F$ is separable $\iff u \not\in K^p$.
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
158327
#define f(g,g2) g##g2
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
31961
Given fields $M/E/F$, why does $[M:F] = [M:E][E:F]$?
154001
$(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
41363
when is f@g not the same as f[g]?
23394
If $G/Z(G)$ is cyclic, then $G$ is abelian
11202
If $g \circ f$ is injective, so is $g$
80199
Do we have always $f(A \cap B) = f(A) \cap f(B)$?
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
97024
If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.