New posts in extension-field

Is there a quadratically closed field strictly between the quadratic closures of $\mathbb{Q}$ and $\mathbb{Q}(\sqrt[3]{2})$?

How to prove that the polynomial $x^2 + x + 1$ is irreducible over $\mathbb Q(\sqrt[3]{2})$?

Does there exist two different fields over $F$ such that they have the same intermediate fields?

Embedding of valued fields

Subfield of $\mathbb{R}$ such that $\Bbb R/K$ is finite. [duplicate]

Is there a subfield $F$ of $\Bbb R$ such that there is an embedding $F(x) \hookrightarrow F$?

A field extension of degree 2 is a Normal Extension.

What is the probability that a rational prime remains prime in $\mathbb Z[i,\sqrt{-3}]$?

Roots of Artin-Schreier equation

The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$

Find all the middle fields of the splitting field of $x^4-2$ over $\mathbb{Q}$ [duplicate]

Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$

Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$

Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$

Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$? [duplicate]

An infinite family of Artin-Schreier polynomials which all split in $\mathbf{F}_q(\!(\theta)\!)$

finding galois extension isomorphic to $\mathbb{Z}_2 \times \mathbb{Z}_4$ and $Q_8$

Why do people study algebraic extension?

Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$

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