Let u be an algebraic element of K whose minimal polynomial in F[x] has prime degree. If E is a field such that F<E<F(u), show that E = F or E=F(u)
126127
A field extension of prime degree
55764
Algebraic closure of $\mathbb F_p$
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
52212
If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
111996
Maximal and Prime Ideal in Z
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
24919
$\mathbb{Q}(\zeta_{10}) $ degree of field extension over $\mathbb{Q}$
94174
Ring of polynomials over a field has infinitely many primes
111248
The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
122952
Degree of extension is equal to linear combination of prime factor multiplicities with prime factor index coefficients in Dedekind domains
85096
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
103763
Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$
31142
Why does $K \leadsto K(X)$ preserve the degree of field extensions?
62615
If F is a finite field, then $F^F=P_F$.
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal