Newbetuts

Let $\alpha$ be a root of $(x^2-a)$ and $\beta$ be a root of $(x^2-b)$. Provide conditions over $a$ and $b$ to have $F=K(\alpha+\beta)$.

Splitting field of $X^n-a$

Geometric interpretation of different types of field extensions?

Degree of splitting field less than n! [duplicate]

I have to find a splitting field of $x^{6}-3$ over $\mathbb{F}_{7}$

Show that $\mathbb{Q}(\sqrt{2 +\sqrt{2}})$ is a cyclic quartic field i.e. is a galois extension of degree 4 with cyclic galois group [duplicate]

Prove $f(x)=x^8-24 x^6+144 x^4-288 x^2+144$ is irreducible over $\mathbb{Q}$

Determine splitting field $K$ over $\mathbb{Q}$ of the polynomial $x^3 - 2$

Galois Group of $x^{4}+7$

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

How many degree $k$, monic polynomials factor completely in $\mathbb{Z}/p\mathbb{Z}$?

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

How to prove that algebraic numbers form a field? [duplicate]

If the Galois group is $S_3$, can the extension be realized as the splitting field of a cubic?

Galois group of $x^4-2$

New posts in splitting-field

Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

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

Finding the $\mathbb{Q}$-automorphisms of the splitting field of $x^p-2$ over $\mathbb{Q}$.

Splitting field of $x^n-a$ contains all $n$ roots of unity

Find the splitting field of $x^4+1$ over $\mathbb Q$.

Let $\alpha$ be a root of $(x^2-a)$ and $\beta$ be a root of $(x^2-b)$. Provide conditions over $a$ and $b$ to have $F=K(\alpha+\beta)$.

Splitting field of $X^n-a$

Geometric interpretation of different types of field extensions?

Degree of splitting field less than n! [duplicate]

I have to find a splitting field of $x^{6}-3$ over $\mathbb{F}_{7}$

Show that $\mathbb{Q}(\sqrt{2 +\sqrt{2}})$ is a cyclic quartic field i.e. is a galois extension of degree 4 with cyclic galois group [duplicate]

Prove $f(x)=x^8-24 x^6+144 x^4-288 x^2+144$ is irreducible over $\mathbb{Q}$

Determine splitting field $K$ over $\mathbb{Q}$ of the polynomial $x^3 - 2$

Galois Group of $x^{4}+7$

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

How many degree $k$, monic polynomials factor completely in $\mathbb{Z}/p\mathbb{Z}$?

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

How to prove that algebraic numbers form a field? [duplicate]

If the Galois group is $S_3$, can the extension be realized as the splitting field of a cubic?

Galois group of $x^4-2$