Existence of totally real number fields of any degree
73669
Totally real Galois extension of given degree
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
28803
Extension of degree 2 with characteristic not 2
76482
Closure of the set of degree $n$ polynomials with $n$ real roots
109801
multiplicative group of infinite fields
146591
Inseparable polynomial over a non-perfect field
84386
Domain strictly contained in the intersection of localizations at the primes of height one
13656
Prove existence of a real root.
7567
Degree of Field Extensions and $F(\alpha)$
103654
A finite field extension that is not simple
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
30817
Is an automorphism of the field of real numbers the identity map?
5893
On the commutative property of multiplication (domain of integers, possibly reals)
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
46572
Degree of a splitting field is no greater than $n!$
108957
Cardinality of a totally ordered union
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$