Is $\mathbb{R}$ a finite field extension?
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
68753
Elements in finite field extensions
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
113175
Why is the algebraic closure of a finite field countable?
86877
Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible
29635
Fields finitely generated as $\mathbb Z$-algebras are finite?
157585
Structure theorem of finite rings
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
16163
Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.
129153
Is it Galois extension?
103654
A finite field extension that is not simple
86234
Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
83586
Finite fields and primitive elements
24919
$\mathbb{Q}(\zeta_{10}) $ degree of field extension over $\mathbb{Q}$
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?