Newbetuts

Why is $\mathbb{Q}(\operatorname{exp}(\frac{2\pi i}{5}))$ a field extension of degree four not five?

Constructive proof of the existence of an algebraic closure

What is the intuition behind defining this isomorphism?

Brauer group of a field of rational numbers

$F[x]/(x^2)\cong F[x]/(x^2 - 1)$ if and only if F has characteristic 2

If $L\mid K$ is a finite extension of fields then K is perfect iff L is perfect

If a normal $K/F$ has no intermediate extensions, then $[K : F]$ is prime

Why is the extension $k(x,\sqrt{1-x^2})/k$ purely transcendental?

Set of elements in $K$ that are purely inseparable over $F$ is a subfield

Solutions to the equation $a^2x-b^2x^2=c^2$

$x^4+x^3+x^2+x+1$ irreducible over $\mathbb F_7$

Finding a Galois extension of $\Bbb Q$ of degree $3$

Can two different roots of an irreducible polynomial generate the same extension?

Non-distributive fields?

In a regular Field $F$. If $p$ is a prime number, all $p$th roots of units (roots of the polynomial $x^p - 1_F$), expect $1_F$, are primitive?

automorphisms of a finite field

New posts in field-theory

Cyclotomic polynomial over a finite prime field [duplicate]

Can we always find field extensions of a given number field and a given degree?

Galois group of $x^6+3$ over $\mathbb Q$

Intermediate field, normal closure and Galois group

Why is $\mathbb{Q}(\operatorname{exp}(\frac{2\pi i}{5}))$ a field extension of degree four not five?

Constructive proof of the existence of an algebraic closure

What is the intuition behind defining this isomorphism?

Brauer group of a field of rational numbers

$F[x]/(x^2)\cong F[x]/(x^2 - 1)$ if and only if F has characteristic 2

If $L\mid K$ is a finite extension of fields then K is perfect iff L is perfect

If a normal $K/F$ has no intermediate extensions, then $[K : F]$ is prime

Why is the extension $k(x,\sqrt{1-x^2})/k$ purely transcendental?

Set of elements in $K$ that are purely inseparable over $F$ is a subfield

Solutions to the equation $a^2x-b^2x^2=c^2$

$x^4+x^3+x^2+x+1$ irreducible over $\mathbb F_7$

Finding a Galois extension of $\Bbb Q$ of degree $3$

Can two different roots of an irreducible polynomial generate the same extension?

Non-distributive fields?

In a regular Field $F$. If $p$ is a prime number, all $p$th roots of units (roots of the polynomial $x^p - 1_F$), expect $1_F$, are primitive?

automorphisms of a finite field