Let $F|K$ be a field extension and $a \in F $ such that $[K(a):K]$ is odd integer
68790
Do we have $K(\beta)=K(\beta^2)$ for field extension of odd degree?
126127
A field extension of prime degree
250
An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root?
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
74681
A finite extension with finitely many intermediate fields is simple
88181
Splitting field of $X^n-a$
42332
Existence of multiplicative inverse in field $\mathbb{Q}(\sqrt{d})$
147069
Intersection of field extensions
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
48093
Irreducible polynomial in field extension
68065
Quadratic extensions in characteristic $2$
883
$K(u,v)$ is a simple extension of fields if $u$ is separable
78561
Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
56439
$f \in K[X]$ of degree $n$ with Galois group $S_n$, why are there no non-trivial intermediate fields of $K \subset K(a)$ with $a$ a root of $f$?
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
28803
Extension of degree 2 with characteristic not 2
92537
Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots