Is the field extension of $\mathbb{R}$ over $\mathbb{Q}$ a countable infinity or uncountable infinity?
17748
Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
42810
Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
56420
Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
60678
Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
34387
Is the number of irreducibles in any number field infinite?
122050
Algebraic extension of perfect field in which every polynomial has a root is algebraically closed
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
140662
Powers of infinite cardinals in the generic extension
78561
Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
71102
Subfields of $\mathbb{C}$ which are connected with induced topology
38489
Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$
112910
Is the set of real numbers really uncountably infinite?
19297
Is the cofinite topology on an uncountable set first countable?
86877
Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible