Newbetuts

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]

$f,g$ be irr poly of degree $m$ and $n$. Show that if $\alpha$ is a root of $f$ in some extension of $F$, then $g$ is ireducible in $F(\alpha)[x]$

Extensions of degree two are Galois Extensions.

Cubic extension and Galois theory [closed]

Solvability in radicals, elementary functions and monodromy/Galois groups

If every polynomial in $k[x]$ has a root in $E$, is $E$ algebraically closed?

How to convert $\Bbb Q(\sqrt 2,\sqrt 3)$ to $\Bbb Q(\alpha)?$

Finding basis of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ over $\mathbb{Q}$

Irreducible polynomial in field extension

Create an explicit extension of the 2-adic metric to $\mathbb{R}$ in which at least $(1,\infty)$ is connected.

Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$ [duplicate]

Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$

Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?

Determine the degree of the extension $\mathbb{Q}(\sqrt{3 + 2\sqrt{2}})$.

Hamel basis for $\mathbb{R}$ over $\mathbb{Q}$ cannot be closed under scalar multiplication by $a \ne 0,1$

Proof that every field is perfect?

New posts in extension-field

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]

$\Omega^1_{K|k}\otimes_KL\rightarrow\Omega^1_{L|k}$ is an isomorphism when $K\subset L$ is finite

Normal Basis Theorem Proof

Computing Galois Group of $\mathbb{Q}(\sqrt{2},\sqrt{3}):\mathbb{Q}$

Is $\mathbb Q(\sqrt{2},\sqrt{3},\sqrt{5})=\mathbb Q(\sqrt{2}+\sqrt{3}+\sqrt{5})$. [duplicate]

$f,g$ be irr poly of degree $m$ and $n$. Show that if $\alpha$ is a root of $f$ in some extension of $F$, then $g$ is ireducible in $F(\alpha)[x]$

Extensions of degree two are Galois Extensions.

Cubic extension and Galois theory [closed]

Solvability in radicals, elementary functions and monodromy/Galois groups

If every polynomial in $k[x]$ has a root in $E$, is $E$ algebraically closed?

How to convert $\Bbb Q(\sqrt 2,\sqrt 3)$ to $\Bbb Q(\alpha)?$

Finding basis of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ over $\mathbb{Q}$

Irreducible polynomial in field extension

Create an explicit extension of the 2-adic metric to $\mathbb{R}$ in which at least $(1,\infty)$ is connected.

Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$ [duplicate]

Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$

Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?

Determine the degree of the extension $\mathbb{Q}(\sqrt{3 + 2\sqrt{2}})$.

Hamel basis for $\mathbb{R}$ over $\mathbb{Q}$ cannot be closed under scalar multiplication by $a \ne 0,1$

Proof that every field is perfect?