Prove if $deg(f)=d$ and $L$ splitting field of $f$ over $K$, $[L:K]\mid d!$
48873
Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$.
78222
Can any monomorphism of a subfield of a splitting field be extended to an automorphism?
48251
Prove that if $n \in \mathbb{N}$, then $\sum_{d|n}{(d(n))^3}=(\sum_{d|n}{d(n)})^2$ where $d(n)$ is the divisor function.
122952
Degree of extension is equal to linear combination of prime factor multiplicities with prime factor index coefficients in Dedekind domains
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
136770
Any field that contains the integers contains the rationals as a subfield (Analysis proof)
81550
Linking two theorems: on algebraic closure and on minimal splitting field
97833
Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
146617
A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
81441
Degree of splitting field divides n!
70951
Prove divisibility law $\,b\mid a,c\,\Rightarrow\, b\mid ka + lc$ for all $k,l\in\Bbb Z$
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
63104
Dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$