New posts in extension-field

$|\operatorname{Aut}(K/F)| \leq [K:F]_s$ holds in general?

Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?

How do extension fields implement $>, <$ comparisons?

Determine the Galois Group of $(x^2-2)(x^2-3)(x^2-5)$

Is $\Bbb Q(\sqrt 2, e)$ a simple extension of $\Bbb Q$?

$L$ is an extension of $K$, if $L$ is a $K$-algebra

Prove that the tensor product of non algebraic extensions is not a field

Example of a nontransitive action of $\operatorname{Aut}(K/\mathbb Q)$ on the roots in $K$ of an irreducible polynomial.

Can we always find field extensions of a given number field and a given degree?

Why is $\mathbb{Q}(\operatorname{exp}(\frac{2\pi i}{5}))$ a field extension of degree four not five?

What is the intuition behind defining this isomorphism?

Dirichlet characters and quadratic fields

If $L\mid K$ is a finite extension of fields then K is perfect iff L is perfect

Why is the extension $k(x,\sqrt{1-x^2})/k$ purely transcendental?

Set of elements in $K$ that are purely inseparable over $F$ is a subfield

Finding a Galois extension of $\Bbb Q$ of degree $3$

Show $Gal(E/\mathbb{Q})\cong \mathbb{\mathbb{Z_2\times Z_2}}$

Is the subextension of a purely transcendental extension purely transcendental over the base field?

Why is the degree of a rational map of projective curves equal to the degree of the homogeneous polynomials?

If a real number can be expressed in terms of complex solutions of cubic equations, can it be expressed in terms of real solutions of cubic equations?