Newbetuts

Exception in the characterization of equality of quadratic extensions when the field is of characteristic $2$.

Calculate the degree of the extension $[\mathbb{Q}(\cos(\frac{2\pi}{p})):\mathbb{Q}]$

Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers. [duplicate]

Unramified p-adic field extension

How can we prove $\mathbb{Q}(\sqrt 2, \sqrt 3, ..... , \sqrt n ) = \mathbb{Q}(\sqrt 2 + \sqrt 3 + .... + \sqrt n )$ [duplicate]

Without the Axiom of Choice, does every infinite field contain a countably infinite subfield?

Finding a basis for $\Bbb{Q}(\sqrt{2}+\sqrt{3})$ over $\Bbb{Q}$.

Prove that an isomorphism $\Phi : F[x] \to F’[x]$ preserves seperability.

Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$. [closed]

Does $\mathbb{F}_p((X))$ has only finitely many extension of a given degree?

Intermediate fields of a finite field extension that is not separable

Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?

$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational

Finding Galois group of $x^6 - 3x^3 + 2$

Do maximal proper subfields of the real numbers exist?

Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?

Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing

New posts in extension-field

Fraction field of $F[X,Y](f)$ isomorphic to $F(X)[Y]/(f)$

Galois groups of $x^3-3x+1$ and $(x^3-2)(x^2+3)$ over $\mathbb{Q}$

Extension fields isomorphic to fields of matrices

Exception in the characterization of equality of quadratic extensions when the field is of characteristic $2$.

Calculate the degree of the extension $[\mathbb{Q}(\cos(\frac{2\pi}{p})):\mathbb{Q}]$

Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers. [duplicate]

Unramified p-adic field extension

How can we prove $\mathbb{Q}(\sqrt 2, \sqrt 3, ..... , \sqrt n ) = \mathbb{Q}(\sqrt 2 + \sqrt 3 + .... + \sqrt n )$ [duplicate]

Without the Axiom of Choice, does every infinite field contain a countably infinite subfield?

Finding a basis for $\Bbb{Q}(\sqrt{2}+\sqrt{3})$ over $\Bbb{Q}$.

Prove that an isomorphism $\Phi : F[x] \to F’[x]$ preserves seperability.

Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$. [closed]

Does $\mathbb{F}_p((X))$ has only finitely many extension of a given degree?

Intermediate fields of a finite field extension that is not separable

Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?

$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational

Finding Galois group of $x^6 - 3x^3 + 2$

Do maximal proper subfields of the real numbers exist?

Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?

Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing