New posts in Extension Field

The Automorphism Group $\Gamma(\mathbb{Q}(\sqrt[n]{2}):\mathbb{Q})$ is trivial if $n$ is odd.

Is there an isomorphism of $F[x]/\langle x^2+a\rangle$ to $F[x]/\langle x^2+x+b\rangle$ just as fields?

Show $\mathbb{Q}( \sqrt{5},\sqrt{7} ) = \mathbb{Q}( \sqrt{5} + \sqrt{7} )$

Proving that $\left[ \mathbb{Q} \left( \sqrt[3]{4+\sqrt{5}} \right ) : \mathbb{Q} \right] = 6$

Degree of a field extension by a transcendental element

For a complex number $\alpha $ which is algebraic over $\Bbb Q$, determining whether $\bar{\alpha}\in \Bbb Q(\alpha)$ or not

What is the concrete meaning of fixing an extension field through a subgroup of automorphisms in $x^3-2$?

How to find the degree of the extension $[\mathbb{Q}(\sqrt[4]{3+2\sqrt{5}}):\mathbb{Q}]$?

Galois Groups and intermediate field extensions

Philosophy of simple field extensions