Newbetuts

Showing that minimal polynomial has the same irreducible factors as characteristic polynomial [duplicate]

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

How do you show that the degree of an irreducible polynomial over the reals is either one or two?

Galois group of the splitting field of the polynomial $x^5 - 2$ over $\mathbb Q$

Let $D$ be an integral domain and let $c\in D$ be irreducible in $D$. Show the ideal $(x,c)$ in $D[x]$ is not principal. [duplicate]

the degree of a splitting field of a polynomial

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

When the group of automorphisms of an extension of fields acts transitively

Quotient ring $\frac{\mathbb{Z}_n[x]}{⟨f(x)^2⟩}$

Why eliminate radicals in the denominator? [rationalizing the denominator] [duplicate]

$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$

How well-studied is origami field theory?

why are subextensions of Galois extensions also Galois?

For which $f,g \in k[t]$, $k[f,g]$ is integrally closed?

Find all the intermediate fields of the splitting field of $x^4 - 2$ over $\mathbb{Q}$

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

New posts in field-theory

Showing that minimal polynomial has the same irreducible factors as characteristic polynomial [duplicate]

Galois correspondence and characteristic subgroups

Showing that $x+x^2$ belongs to an ideal in $\mathbb{Z}_2[x]$

A proof of Artin's linear independence of characters

Why isn't the perfect closure separable?

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

How do you show that the degree of an irreducible polynomial over the reals is either one or two?

Galois group of the splitting field of the polynomial $x^5 - 2$ over $\mathbb Q$

Let $D$ be an integral domain and let $c\in D$ be irreducible in $D$. Show the ideal $(x,c)$ in $D[x]$ is not principal. [duplicate]

the degree of a splitting field of a polynomial

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

When the group of automorphisms of an extension of fields acts transitively

Quotient ring $\frac{\mathbb{Z}_n[x]}{⟨f(x)^2⟩}$

Why eliminate radicals in the denominator? [rationalizing the denominator] [duplicate]

$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$

How well-studied is origami field theory?

why are subextensions of Galois extensions also Galois?

For which $f,g \in k[t]$, $k[f,g]$ is integrally closed?

Find all the intermediate fields of the splitting field of $x^4 - 2$ over $\mathbb{Q}$

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