Show that the algebraic extension $K(\alpha,\beta)/K$ is simple if $\alpha$ is separable over $K$
883
$K(u,v)$ is a simple extension of fields if $u$ is separable
28313
Intermediate ring between a field and an algebraic extension.
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
137715
If $[L:K]$ is prime, show that $L/K$ is a simple extension.
16163
Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.
24247
Ring Inside an Algebraic Field Extension
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
143138
All models of $\mathsf{ZFC}$ between $V$ and $V[G]$ are generic extensions of $V$
118874
If $v$ is algebraic over $K(u)$, for some $u\in F$, and $v $ is transcendental over $K$, then $u$ is algebraic over $K(v)$
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
56143
Proof of a basic $AC_\omega$ equivalence
1060
Minimal polynomial of intermediate extensions under Galois extensions.
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
46730
How to show $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$?
21578
Showing the minimal polynomial for an element in an extension field is the same as the minimal polynomial of a linear transformation.
19525
Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8