If $F\subseteq L\subseteq K$ are fields, then show that $[K : F]_s = [K: L]_s[L: F]_s$ and $[K: F]_i = [K: L]_i[L: F]_i$
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
146617
A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
78561
Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
133561
show that if $K$ is a field then $K[x]$ is principal
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
128305
$PGL(n, F)=PSL(n, F)$
41099
If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
107207
$A\subseteq B\subseteq C$ ring extensions, $A\subseteq C$ finite/finitely-generated $\Rightarrow$ $A\subseteq B$ finite/finitely-generated?