New posts in field-theory

Simplify $\mathbb{Q}(\pi^3+\pi^2, \pi^8+\pi^5)$

Showing $[K(x):K(\frac{x^5}{1+x})]=5$?

An element is integral iff its minimal polynomial has integral coefficients.

Finite Field Extensions and the Sum of the Elements in Proper Subextensions (Follow-Up Question)

Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)

Intersection of field extensions

Extension of isomorphism of fields

Is there a subfield of $\mathbb{R}$ that is a proper elementary extension of $\mathbb{Q}$?

Polynomial rings -- Inherited properties from coefficient ring

A finite field extension $K\supset\mathbb Q$ contains finitely many roots of unity

Computing a uniformizer in a totally ramified extension of $\mathbb{Q}_p$.

Infinite number of intermediate fields between K(u,v) and K

In a field extension, if each element's degree is bounded uniformly by $n$, is the extension finite?

Suppose $K/F$ is a Galois extension of degree $p^m$. Then there is a chain of extensions $F \subseteq F_1 \subseteq \cdots F_m = K$ each of degree $p$

On the unicity of splitting field

Generic Element of Compositum of Two Fields [duplicate]

Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

$f$ is irreducible $\iff$ $G$ act transitively on the roots

How is the degree of the minimal polynomial related to the degree of a field extension?